<PAGE>
 
---------
  ZENIX
 Income
Fund Inc.
---------

                                    [LOGO]



                                                       Semi-Annual Report
                                                       September 30, 1998
<PAGE>
 
--------------------------------------------------------------------------------

                                     [LOGO]

                             Zenix Income Fund Inc.

                                            [PHOTO]          [PHOTO]

                                            HEATH B.         JOHN C.
                                            MCLENDON         BIANCHI

                                            Chairman         Vice President and
                                                             Investment Officer

Dear Shareholder:

We are pleased to provide you with the semi-annual report for the Zenix Income
Fund Inc. ("Fund") for the period ended September 30, 1998. Over the past six
months the Fund paid income dividends totaling $0.36 per share. The table below
shows the annualized distribution rate and six-month total return for the Fund
based on its September 30, 1998 net asset value ("NAV") per share and its New
York Stock Exchange ("NYSE") closing price.

                                       Annualized              Six-Month
         Price Per Share            Distribution Rate        Total Return
         ---------------            -----------------        ------------
         $6.05 (NAV)                    11.50%                  (8.34%)
         $6.31 (NYSE)                   11.03%                 (11.24%)

The Fund generated a negative total return on NAV of 8.34% for the six-months
ended September 30, 1998. The Fund's performance is comparable to the six-month
average total return of a negative 8.52% for closed-end high yield bond funds as
reported by Lipper Analytical Services, Inc. (Lipper is an independent mutual
fund performance tracking organization). A full discussion of the past six
month's economic and market conditions as well as the investment strategy
pursued by the Fund during this time follows.


                                       1

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Market and Economic Overview

The high yield bond market generated weak results in the past six months ended
September 30, 1998 and underperformed all other U.S. bond market sectors. As
many investors became more convinced that the emerging market crisis would
contribute to an economic slowdown in the U.S. beginning in the second half of
1998, the 30-year U.S. Treasury bond generated very strong performance results.
The higher-quality, high-yield issues generated the strongest results given
their potential to better weather any slowdown in U.S. economic growth. On the
other hand, the lowest-quality high yield bond issues generated the worst
returns in the U.S. bond market, which was not surprising given their higher
vulnerability to any potential slowdown in economic growth. By the end of
September, the high-yield bond market had reached relative valuation levels last
seen in the recession of 1990 and 1991. We believe that the high yield bond
market's recent sell-off has been more of a function of very poor short-term
demand and less a function of any major deterioration in U.S. economic growth.

The year-to-date total of newly issued high yield bonds was roughly $120
billion, which is double last year's figure of $60 billion. The year-to-date $15
billion of cash inflows into open-end high yield bond mutual funds, while above
last year's total of $8 billion, was clearly insufficient to counterbalance the
extremely heavy new issue calendar. We believe this short-term imbalance will
eventually correct itself with reduced new issuance. Moreover, the recent
problems among money domestic hedge funds has also negatively influenced the
financial markets as they continue to liquidate their positions.

While the current U.S. economy remains generally supportive of a broad range of
U.S. companies and inflation continues to be modest, there is some concern that
the Asian economic crisis as well as recent financial market turmoil may force
the U.S. economy into a recession. So far, we have not seen, nor do we expect to
see, a material increase in bankruptcies among most companies that issue
high-yield bonds.

While there may be some increase in failure rates of some companies, we believe
it will be confined to the more vulnerable lower quality companies in industries
marked by significant competition and declining prices. Yet, there is no
question that the U.S. economy is slowing down somewhat, especially among some


                                       2

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<PAGE>
 
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commodity companies that either export products overseas or compete with
lower-cost imports.

We believe that it's still an open question as to whether or not Asia's problems
will have a meaningfully negative impact on overall U.S. economic growth.
Nevertheless, the Federal Reserve Board ("Fed") remains vigilant about the
potential for a pronounced deterioration in U.S. economic growth. The Fed has
recently begun reducing short-term interest rates to prevent the current
slowdown from turning into a major recession. We believe this monetary policy
change on the part of the Fed should go a long way towards stabilizing the
financial markets both here and abroad.

Portfolio Strategy and Market Outlook

The Zenix Income Fund remains cautiously positioned with a heavy emphasis in
better quality, intermediate maturity "B" and "BB" rated high-yield bonds. As of
September 30, 1998, the Fund's average maturity on a call-adjusted basis was
approximately 6.5 years. (This measure of average maturity takes into account
that certain bonds are callable earlier than their stated maturity.) In
addition, the Fund continued to emphasize telecommunications issues as well as
cable and media issues.

As high yield bond spreads continued to widen during the past six months, we
began to take advantage of what we believed were attractively priced "B" rated
issues. Given the continued problems in Asia, we plan to remain underweighted in
basic commodity industries such as steel, forest products and petrochemicals,
industries that have been negatively affected by deflationary trends. (Deflation
is when prices actually fall. Deflation should not be confused with
disinflation, which is the slowing down of the rate at which prices increase.)

We believe that the Fund is appropriately positioned for current economic
conditions. While we still expect economic growth to slow and corporate profit
margins to deteriorate for the remainder of 1998, we do not anticipate a
recession at this time, especially in light of the Fed's actions in lowering
short-term interest rates. Moreover, given the higher volatility in the
financial markets, we will continue to maintain what we consider to be the
Fund's relatively sound credit quality orientation.


                                       3

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<PAGE>
 
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Thank you for investing in the Zenix Income Fund. We look forward to continuing
to help you pursue your investment goals. Should you have any questions about
your investment in the Fund, please call the First Data Investor Services Group
Inc. at (800) 331-1710.

Sincerely,


/s/ Heath B. McLendon                                /s/ John C. Bianchi, CFA

Heath B. McLendon                                    John C. Bianchi, CFA
Chairman                                             Vice President and
                                                     Investment Officer

October 20, 1998


                                       4

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<PAGE>
 
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--------------------------------------------------------------------------------
Take Advantage of the Fund's Dividend Reinvestment Plan!

      Did you know that Fund investors who reinvest their dividends are taking
advantage of one of the most effective wealth-building tools available today?
Systematic investments put time to work for you through the strength of
compounding.

      As an investor in the Fund, you can participate in its Dividend
Reinvestment Plan ("Plan"), a convenient, simple and efficient way to reinvest
your dividends and capital gains, if any, in additional shares of the Fund. For
more detailed information about the Fund's Plan, a complete description of the
Plan begins on page 29. Below is a summary of how the Plan works.

Plan Summary

      If you are a Plan participant who has not elected to receive your
dividends in the form of a cash payment then your dividends and capital gains
distributions will be reinvested automatically in additional shares of the Fund.

      The number of common stock shares in the Fund you will receive in lieu of
a cash dividend is determined in the following manner. If the market price of
the common stock is equal to or higher than 98% of the net asset value ("NAV")
per share at the time of valuation, you will be issued shares for the equivalent
of either 98% of the most recently determined NAV per share or 95% of the market
price, whichever is greater.

      If 98% of the NAV per share at the time of valuation is greater than the
market price of the common stock, or if the Fund declares a dividend or capital
gains distribution payable only in cash, the Fund will buy common stock for your
account in the open market or whichever exchange the Fund is listed.

      If the Fund begins to purchase additional shares in the open market and
the market price of the shares subsequently rises above 98% of the NAV before
the purchases are completed, the Fund will attempt to cancel any remaining
orders and issue the remaining dividend or distribution in shares at 98% of the
Fund's NAV per share. In that case, the number of Fund shares you receive will
be based on the weighted average of prices paid for shares purchased in the open
market and the price at which the Fund issues the remaining shares.

      To find out more detailed information about the Plan and about how you can
participate, please call First Data Investors Services Group, Inc. at (800)
331-1710.
--------------------------------------------------------------------------------


                                       5

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<PAGE>
 
[LOGO]                                                   Schedule of Investments
                                                  September 30, 1998 (unaudited)
================================================================================

<TABLE>
<CAPTION>
  Face  
 Amount     Rating                     Security                                      Value 
---------------------------------------------------------------------------------------------- 
<S>           <C>   <C>                                                           <C> 
CORPORATE BONDS AND NOTES -- 93.2%
Aerospace/Defense -- 1.7%
$2,500,000    Ba2*  Airplanes Pass Through Trust, Corporate Collateralized
                      Mortgage Obligation, 10.875% due 3/15/19 .................  $  2,652,200
                                                                                  ------------

Banking -- 1.5%
 1,925,000    Ba3*  First Nationwide Parent Holdings Ltd., Sr. Notes,
                      12.500% due 4/15/03 ......................................     2,223,375
                                                                                  ------------
Broadcasting/Cable -- 11.4%
   925,000    BB-   Century Communications Corp., Sr. Notes,                                    
                      8.750% due 10/1/07 .......................................       980,500  
 1,500,000    B2*   Comcast UK Cable, Debentures, step bond to yield                           
                      11.175% due 11/15/07 .....................................     1,216,875  
                    CSC Holdings Inc., Sr. Sub. Debentures:                                     
 2,975,000    BB-     9.875% due 2/15/13 .......................................     3,302,250  
 1,000,000    BB-     10.500% due 5/15/16 ......................................     1,167,500  
   200,000    BB+     7.625% due 7/15/18 .......................................       193,500  
   550,000    BB-     9.875% due 4/1/23 ........................................       610,500  
                    Rogers Cablesystems of America, Inc.:                                       
 1,850,000    BB+     Sr. Notes, Series B, 10.000% due 3/15/05 .................     2,039,625  
 1,000,000    BB+     Sr. Sub. Debentures, 10.000% due 12/1/07 .................     1,102,500  
 2,100,000    BB-     Sr. Sub. Debentures, 11.000% due 12/1/15 .................     2,436,000  
   455,000    CCC+  Telemundo Holdings Inc., Sr. Discount Notes,                                
                      step bond to yield 11.120% due 8/15/08+ ..................       241,150  
                    TV Azteca SA, Guaranteed Sr. Notes:                                         
   525,000    Ba3*    Series A, 10.125% due 2/15/04 ............................       383,250  
   950,000    Ba3*    Series B, 10.500% due 2/15/07 ............................       703,000  
 6,050,000    B     United International Holdings Inc., Sr. Discount Notes,                     
                      step bond to yield 11.136% due 2/15/08+ ..................     2,904,000  
                                                                                  ------------  
                                                                                    17,280,650  
                                                                                  ------------  
Building/Construction -- 0.6%
   500,000    BB    Building Material Corp., Sr. Notes, 7.750% due 7/15/05+ ...        477,500
   400,000    B+    Nortek Inc., Sr. Notes, 9.125% due 9/1/07 ..................       395,000
                                                                                  ------------
                                                                                       872,500
                                                                                  ------------
Cellular and Other Wireless -- 8.6%
 3,275,000    B3*   Clearnet Communications Inc., Sr. Discount Notes,
                      step bond to yield, 12.200% due 12/15/05 .................     2,726,438
</TABLE>

                       See Notes to Financial Statements.


                                       6
<PAGE>
 
[LOGO]                                       Schedule of Investments (continued)
                                                  September 30, 1998 (unaudited)
================================================================================

<TABLE>
<CAPTION>
  Face                                                                                         
 Amount     Rating                     Security                                      Value 
---------------------------------------------------------------------------------------------- 
<S>           <C>  <C>                                                            <C> 
Cellular and Other Wireless-- 8.6% (continued)
                   Dolphin Telecom PLC, Sr. Discount Notes:
$1,600,000    B-      Step bond to yield 11.416% due 6/1/08+ ...................  $   784,000
 1,125,000++  B-      Step bond to yield 11.625% due 6/1/08 ....................      635,908
 2,675,000    B-    Iridium LLC Capital Corp., Guaranteed Notes,
                      14.000% due 7/15/05 ......................................     2,387,438
 2,500,000    B-    Millicom International Cellular S.A., Sr. Discount Notes,
                      step bond to yield 15.406% due 6/1/06 ....................     1,631,250
   725,000    B2*   Nextel Communications Inc., Sr. Discount Notes,
                      step bond to yield 8.918% due 8/15/04 ....................       696,000
 1,700,000    Ba3*  Orange PLC, Sr. Notes, 8.000% due 8/1/08 ...................     1,666,000
 2,075,000    NR    Pagemart Inc., Sr. Discount Notes,
                      step bond to yield 11.250% due 2/1/08 ....................     1,154,219
                    Telesystems International Wireless Corp., Sr. Discount Notes:
 1,300,000    CCC+    Step bond to yield 12.460% due 6/30/07 ...................      754,000
 1,100,000    CCC+    Step bond to yield 11.064% due 11/1/07 ...................      572,000
                                                                                  ------------
                                                                                    13,007,253
                                                                                  ------------
Diversified/Conglomerate Manufacturing -- 3.0%
   675,000    BB-   Cia Latino Americana, Guaranteed Sr. Notes,
                      11.625% due 6/1/04+ ......................................       498,656
   450,000    B-    Eagle-Picher Industrial Inc., Sr. Sub. Notes, 9.375%
                      due 3/1/08 ...............................................       416,250
   950,000    B3*   Interlake Corp., Sr. Sub. Debentures, 12.125% due 3/1/02 ...       952,375
 1,000,000    B2*   Intertek Finance PLC., Sr. Sub. Notes, Series B,
                      10.250% due 11/1/06 ......................................       912,500
 1,100,000    B     Outboard Marine Corp., Sr. Notes, 10.750% due 6/1/08 .......     1,065,625
   700,000    B+    Park-Ohio Industries, Sr. Sub. Notes, 9.250% due 12/1/07 ...       701,750
                                                                                  ------------
                                                                                     4,547,156
                                                                                  ------------
Diversified/Conglomerate Services -- 0.7%
   650,000    NR    Axiohm Transaction Solutions, Sr. Sub. Notes,
                      9.750% due 10/1/07 .......................................       582,563
   500,000    B-    Outsourcing Solutions, Sr. Sub. Notes, 11.000% due 11/1/06 .       471,875
                                                                                  ------------
                                                                                     1,054,438
                                                                                  ------------
Electric Utilities -- 3.6%
 2,350,000    Ba1*  AES Corp., Sr. Sub. Notes, 8.500% due 11/1/07 ..............     2,232,500
                    Calpine Corp., Sr. Notes:
 1,350,000    Ba2*    10.500% due 5/15/06 ......................................     1,471,500
   750,000    Ba2*    8.750% due 7/15/07 .......................................       768,750
</TABLE>


                       See Notes to Financials Statements


                                       7
<PAGE>
 
[LOGO]                                       Schedule of Investments (continued)
                                                  September 30, 1998 (unaudited)
================================================================================

<TABLE>
<CAPTION>
  Face                                                                                         
 Amount     Rating                     Security                                      Value 
---------------------------------------------------------------------------------------------- 
<S>           <C>   <C>                                                           <C> 
Electric Utilities -- 3.6% (continued)
$  795,090    BB    Midland Cogeneration Venture Limited Partnership,
                      Midland Funding, Sr. Secured Lease Obligation Bond,
                      Series C, 10.330% due 7/23/02 ............................  $    846,770 
   200,000    BB-   Niagara Mohawk Power, step bond to yield 8.229% due 7/1/10..       141,750 
                                                                                  ------------ 
                                                                                     5,461,270 
                                                                                  ------------ 
Electronics-Computers -- 6.2%                                                                  
   725,000    B     Celestica International Inc., Sr. Sub. Notes,                              
                      10.500% due 12/31/06 .....................................       773,938 
 1,500,000    B     Fairchild Semiconductor Inc., Sr. Sub. Notes,                              
                      10.125% due 3/15/07 ......................................     1,350,000 
 1,000,000    B-    Graphic Controls Corp., Sr. Sub. Notes, 12.000%                            
                      due 9/15/05 ..............................................     1,120,000 
                    Unisys Corp., Sr. Notes:                                                   
 1,800,000    Ba3*    12.000% due 4/15/03 ......................................     2,002,500 
 2,325,000    Ba3*    11.750% due 10/15/04 .....................................     2,615,625 
   505,000    Ba3*    7.875% due 4/1/08 ........................................       505,000 
 1,200,000    B-    Viasystems Inc., Sr. Sub. Notes, 9.750% due 6/1/07 .........     1,026,000 
                                                                                  ------------ 
                                                                                     9,393,063 
                                                                                  ------------ 
Finance -- 3.2%                                                                                
 1,500,000    B     Amresco Inc., Sr. Sub. Notes, Series A, 10.000%                            
                      due 3/15/04 ..............................................     1,248,750 
 1,000,000    B2*   Ocwen Capital Trust, Guaranteed Notes, 10.875% due 8/1/27 ..       912,500 
 2,750,000    BB-   Ocwen Financial Corp., Notes, 11.875% due 10/1/03 ..........     2,715,625 
                                                                                  ------------ 
                                                                                     4,876,875 
                                                                                  ------------ 
Foods -- 1.8%                                                                                  
   850,000    B-    B&G Foods Inc., Sr. Sub. Notes, 9.625% due 8/1/07 ..........       786,250 
   400,000    Ba3*  Carrols Corp., Sr. Notes, 11.500% due 8/15/03 ..............       419,000 
 1,325,000    B     Imperial Holly Corp., Sr. Sub Notes, 9.750% due 12/15/07 ...     1,262,063 
   300,000    B     SC International Services Inc., Guaranteed Sr. Notes,                      
                      9.250% due 9/1/07 ........................................       291,000 
                                                                                  ------------ 
                                                                                     2,758,313 
                                                                                  ------------ 
Grocery/Convenience Stores -- 0.5%                                                             
   750,000    B+    Jitney-Jungle Stores, Sr. Notes, 12.000% due 3/1/06 ........       828,750 
                                                                                  ------------ 
Healthcare/Drugs/Hospital Supplies -- 9.6%                                                     
   300,000    B-    Alaris Medical, Sr. Discount Notes,                                        
                      step bond to yield 11.125% due 8/1/08 ....................       132,000 
</TABLE>
                                                                                
                       See Notes to Financial Statements                        
                                                                                
                                                                                
                                       8                                        
<PAGE>
 
[LOGO]                                       Schedule of Investments (continued)
                                                  September 30, 1998 (unaudited)
================================================================================

<TABLE>
<CAPTION>
  Face   
 Amount     Rating                     Security                                      Value 
---------------------------------------------------------------------------------------------- 
<S>           <C>   <C>                                                           <C> 
Healthcare/Drugs/Hospital Supplies -- 9.6% (continued)                                         
                    Columbia/HCA Healthcare, Notes:                                           
$  600,000    BBB     7.000% due 7/1/07 ........................................  $    580,500 
   200,000    BBB     7.250% due 5/20/08 .......................................       196,000 
   300,000    BBB     6.630% due 7/15/45 .......................................       297,000 
                    ICN Pharmaceuticals Inc., Sr. Notes:                                       
 1,800,000    BB      9.250% due 8/15/05 .......................................     1,786,500 
   275,000    BB      8.750% due 11/15/08+ .....................................       272,938 
                    Integrated Health Services Inc., Sr. Sub. Notes:                           
   715,000    B2*     9.500% due 9/15/07 .......................................       691,763 
 1,650,000    B2*     9.250% due 1/15/08 .......................................     1,579,875 
 5,000,000    B-    Magellan Health Services Inc., Sr. Sub. Notes,                             
                      9.000% due 2/15/08+ ......................................     4,306,250 
 1,650,000    B-    Mariner Post Acute Network, Sr. Sub. Notes,                                
                      9.500% due 11/1/07 .......................................     1,538,625 
                    Sun Healthhcare Group Inc., Sr. Sub Notes:                                 
 1,700,000    B2*     9.500% due 7/1/07 ........................................     1,555,500 
 1,900,000    B2*     9.375% due 5/1/08 ........................................     1,719,500 
                                                                                  ------------ 
                                                                                    14,656,451 
                                                                                  ------------ 
Hotel, Casinos and Gaming -- 4.3%                                                              
 1,500,000    B     Aztar Corp., Sr. Sub. Notes, 13.750% due 10/1/04 ...........     1,702,500 
 3,000,000    B-    Courtyard By Marriott II, Sr. Secured Notes,                               
                      10.750% due 2/1/08 .......................................     3,165,000 
   800,000    BB    Grand Casinos, First Mortgage, 10.125% due 12/1/03 .........       852,000 
   620,000    BB+   Mohegan Tribal Gaming Authority, Sr. Secured Notes,                        
                      13.500% due 11/15/02 .....................................       800,575 
                                                                                  ------------ 
                                                                                     6,520,075 
                                                                                  ------------ 
Insurance -- 1.1%                                                                              
 1,000,000    BB+   SIG Capital Trust, Guaranteed Notes, 9.500% due 8/15/27 ....       972,500 
   650,000    BB-   Veritas Capital Trust, Guaranteed Notes,                                   
                      10.000% due 1/1/28+ ......................................       632,125 
                                                                                  ------------ 
                                                                                     1,604,625 
                                                                                  ------------ 
Leisure -- 0.7%                                                                                
 1,100,000    B3*   SFX Entertainment Inc., Sr. Sub Notes, 9.125% due 2/1/08 ...     1,045,000 
                                                                                  ------------ 
Machinery -- 0.3%                                                                              
   500,000    B-    Alvey Systems Inc., Sr. Sub. Notes, 11.375% due 1/31/03 ....       499,375 
                                                                                  ------------ 
</TABLE>                                                                        
                                                                                
                       See Notes to Financial Statements                        
                                                                                
                                                                                
                                       9                                        
<PAGE>
 
[LOGO]                                       Schedule of Investments (continued)
                                                  September 30, 1998 (unaudited)
================================================================================

<TABLE>                                                                         
<CAPTION>                                                                       
  Face                                                                          
 Amount     Rating                     Security                                      Value 
---------------------------------------------------------------------------------------------- 
<S>          <C>    <C>                                                           <C> 
Metals/Mining -- 0.3%                                                                          
$  400,000   B-     Haynes International Inc., Sr. Notes, 11.625% due 9/1/04 ...  $    445,000 
                                                                                  ------------ 
Oil/Natural Gas -- 4.4%                                                                        
   500,000   B      Canadian Forest Oil Ltd., Sr. Sub. Notes, 8.750%                           
                      due 9/15/07 ..............................................       455,000 
 1,300,000   B+     Clark USA Inc., Sr. Notes, 10.875% due 12/1/05 .............     1,248,000 
                    Ocean Energy Inc., Sr. Sub Notes:                                          
   800,000   BB-      10.375% due 10/15/05 .....................................       842,000 
   400,000   BB-      9.750% due 10/1/06 .......................................       415,000 
   450,000   BB-      8.875% due 7/15/07 .......................................       452,250 
   850,000   B+     Parker Drilling Co., Sr. Notes, 9.750% due 11/15/06 ........       792,625 
 1,675,000   BB-    Santa Fe Energy Resources Inc., Sr. Sub. Debentures,                       
                      11.000% due 5/15/04 ......................................     1,779,688 
   700,000   B2*    Stone Energy Corp., Sr. Sub. Notes, 8.750% due 9/15/07 .....       672,000 
                                                                                  ------------ 
                                                                                     6,656,563 
                                                                                  ------------ 
Oil Services -- 0.9%                                                                           
   500,000   BB+    J. Ray McDermott SA, Sr. Sub. Notes, 9.375% due 7/15/06 ....       527,500 
   900,000   BB     Pride Petroleum Services Inc., Sr. Notes, 9.375%                           
                      due 5/1/07 ...............................................       848,250 
                                                                                  ------------ 
                                                                                     1,375,750 
                                                                                  ------------ 
Packaging/Containers -- 0.9%                                                                   
   575,000   B      Huntsman Packaging Corp., Sr. Notes, 9.125% due 10/1/07+ ...       510,312 
 1,000,000++ B      Impress Metal Packaging Holdings, Sr. Sub. Notes,                          
                      9.875% due 5/29/07 .......................................       598,300 
   250,000   B-     Tekni-Plex Inc., Sr. Sub Notes, 9.250% due 3/1/08+ .........       241,250 
                                                                                  ------------ 
                                                                                     1,349,862 
                                                                                  ------------ 
Paper/Forest Products and Printing -- 3.4%                                                     
 4,695,000   B+     S.D. Warren Co., Sr. Sub. Notes, 12.000% due 12/15/04 ......     5,170,369 
                                                                                  ------------ 
Personal Care Products/Cosmetics -- 1.1%                                                       
   900,000   B-     Revlon Consumer Products, Sr. Sub. Notes,                                  
                      8.625% due 2/1/08 ........................................       886,500 
 1,100,000   B-     Revlon Worldwide Series B, Sr. Disc. Notes,                                
                      zero coupon to yield 12.940% due 3/15/01 .................       844,250 
                                                                                  ------------ 
                                                                                     1,730,750 
                                                                                  ------------ 
Pollution Control -- 0.7%                                                                      
 1,000,000   B+     Allied Waste North America Inc., Sr. Sub. Notes,                           
                      10.250% due 12/1/06 ......................................     1,092,500 
                                                                                  ------------ 
</TABLE>                                                                        
                                                                                
                       See Notes to Financial Statements                        
                                                                                
                                                                                
                                       10                                       
<PAGE>
 
[LOGO]                                       Schedule of Investments (continued)
                                                  September 30, 1998 (unaudited)
================================================================================

<TABLE>
<CAPTION>
  Face 
 Amount     Rating                     Security                                      Value 
---------------------------------------------------------------------------------------------- 
<S>           <C>   <C>                                                           <C> 
Publishing -- 1.1%                                                                             
$1,100,000++  B     Middleweb PLC, Sr. Notes, 10.500% due 5/30/08 ..............  $  1,626,334 
                                                                                  ------------ 
                                                                                               
Real Estate -- 1.2%                                                                            
   675,000    B-    BF Saul REIT, Sr. Notes, 9.750% due 4/1/08 .................       592,312 
 1,115,000    Baa3* Trizec Finance Ltd., Sr. Notes, 10.875% due 10/15/05 .......     1,234,863 
                                                                                  ------------ 
                                                                                     1,827,175 
                                                                                  ------------ 
Retail -- 1.4%                                                                                 
   300,000    B-    Advance Holdings Corp., Sr. Discount Notes,                                
                      step bond to yield 12.592% due 4/15/09+ ..................       174,000 
 1,000,000    B-    Advance Stores Co., Inc. Sr. Sub. Notes,                                   
                      10.250% due 4/15/08+ .....................................       980,000 
 1,150,000    B-    US Office Products Co., Sr. Sub. Notes, 9.750%                             
                      due 6/15/08+ .............................................       986,125 
                                                                                  ------------ 
                                                                                     2,140,125 
                                                                                  ------------ 
Telecommunications -- 15.9%                                                                    
                    Colt Telecommunications Group PLC:                                         
   250,000++  B       Sr. Notes, 10.125% due 11/30/07 ..........................       416,355 
 2,000,000    B       Step bond to yield 11.976% due 12/15/06 ..................     1,580,000 
 2,450,000    NR    E.Spire Communications, Sr. Discount Notes,                                
                      step bond to yield 11.175% due 7/1/08 ....................     1,261,750 
                    Esprit Telecom Group PLC, Sr. Notes:                                       
   700,000    B-      11.500% due 12/15/07 .....................................       640,500 
   600,000++  B-      11.500% due 12/15/07 .....................................       317,697 
   400,000    B-      10.875% due 6/15/08 ......................................       360,000 
 1,025,000    NR    Facilicom International Inc., Sr. Notes, 10.500%                           
                      due 1/15/08 ..............................................       896,875 
 1,000,000    B     Hermes Eurorail Telecommunications Inc., Sr. Notes,                        
                      11.500% due 8/15/07 ......................................     1,050,000 
   775,000    B+    Impsat Corp., Sr. Notes, 12.375% due 6/15/08 ..............        615,156 
 2,275,000    B     Intermedia Communications, Sr. Discount Notes,                             
                      step bond to yield 12.351% due 5/15/06 ...................     1,854,125 
 1,650,000    B     Level 3 Communications, Sr. Notes, 9.125% due 5/1/08 ......      1,559,250 
                    Metronet Communications Inc.:                                              
 4,800,000    B       Sr. Discount Notes, step bond to yield 10.049%                           
                      due 6/15/08 ..............................................     2,652,000 
 1,650,000    B       Sr. Notes, 12.000% due 8/15/07 ...........................     1,749,000 
 1,150,000    B     Nextlink Communications, Sr. Notes, 12.500% due 4/15/06 ...      1,244,875 
 1,200,000    B-    Psinet Inc., Sr. Notes, 10.000% due 2/15/05 ...............      1,206,000 
 2,750,000    BB+   Qwest Communications International Inc., Sr. Discount Notes,               
                      step bond to yield 9.351% due 10/15/07 ...................     2,110,625 
                    RCN Corp.:                                                                 
 1,775,000    B3*     Sr. Discount Notes, step bond to yield 11.141%                             
                        due 10/15/07 ...........................................       985,125 
 1,000,000    B3*     Sr. Notes, 10.000% due 10/15/07 ........................         940,000 
</TABLE>                                                                        
                                                                                
                       See Notes to Financial Statements                        
                                                                                
                                                                                
                                       11                                       
<PAGE>
 
[LOGO]                                       Schedule of Investments (continued)
                                                  September 30, 1998 (unaudited)
================================================================================

<TABLE>                                                                         
<CAPTION>                                                                       
  Face                                                                          
 Amount     Rating                     Security                                      Value 
---------------------------------------------------------------------------------------------- 
<S>           <C>   <C>                                                           <C> 
Telecommunications -- 15.9% (continued)                                                        
$1,625,000    NR    Splitrock Services, Units, 11.750% due 7/15/08 .............  $  1,470,625 
   825,000    NR    Versatel Telecommunications, Units, 13.250% due 5/15/08 ....       785,812 
   850,000    NR    Wam!Net Inc., step bond to yield 13.327% due 3/1/05 ........       476,000 
                                                                                  ------------ 
                                                                                    24,171,770 
                                                                                  ------------ 
Textiles -- 0.2%                                                                               
   800,000++  B     Texon International, Sr. Notes, 10.000% due 2/1/08+ ........       373,339 
                                                                                  ------------ 
                                                                                               
Transportation -- 2.9%                                                                         
   300,000   B+     American Reefer Co. Ltd., 1st Mortgage, 10.250%                            
                      due 3/1/08+ ..............................................       252,000 
 2,805,000   BB-    Sea Containers Ltd., Sr. Sub. Debentures,                                  
                      12.500% due 12/1/04 ......................................     3,145,106 
   800,000   B+     Stena Line AB, Sr. Notes, 10.625% due 6/1/08 ...............       722,000 
   425,000   B+     TBS Shipping International Ltd., First Mortgage,                           
                      10.000% due 5/1/05 .......................................       318,750 
                                                                                  ------------ 
                                                                                     4,437,856 
                                                                                  ------------ 
                    TOTAL CORPORATE BONDS AND NOTES                                            
                    Cost -- $146,667,323) ......................................   141,678,762 
                                                                                  ------------ 
                                                                                               
<CAPTION>                                                                                      
 Shares                                Security                                      Value 
---------------------------------------------------------------------------------------------- 
<S>                 <C>                                                                <C> 
PREFERRED STOCKS -- 0.3%                                                                       
Banking -- 0.3%                                                                                
    20,100          California Federal Preferred Capital Corp., Series A,                      
                      Exchange 9.125% (Cost-- $502,500) ........................       513,806 
                                                                                  ------------ 
WARRANTS# -- 0.6%                                                                              
Broadcasting/Cable -- 0.0%                                                                     
     2,450          UIH Australia Inc., Expire 5/15/06 .........................        12,250 
                                                                                  ------------ 
Cellular and Other Wireless -- 0.2%                                                            
     9,735          Clearnet Communications Inc., Expire 9/15/05+ ..............        58,410 
     1,000          Globalstar Telecommunications, Expire 2/15/04 ..............       105,000 
     1,000          Iridium World Communications Ltd., Expire 7/15/05 ..........       140,000 
     7,130          Pagemart Inc., Expire 12/31/03+ ............................        42,780 
                                                                                  ------------ 
                                                                                       346,190 
                                                                                  ------------ 
Telecommunications -- 0.4%                                                                     
     1,750          Allegiance Telecommunications Inc., Expire 2/3/08 ..........        21,000 
     2,000          Colt Telecommunications Warrants, Expire 12/31/06 ..........       400,000 
</TABLE>                                                                        
                                                                                
                       See Notes to Financial Statements                        
                                                                                
                                                                                
                                       12                                       
<PAGE>
 
[LOGO]                                       Schedule of Investments (continued)
                                                  September 30, 1998 (unaudited)
================================================================================

<TABLE>                                                                         
<CAPTION>                                                                       
  Shares                               Security                                          Value 
---------------------------------------------------------------------------------------------- 
<S>                 <C>                                                           <C> 
Telecommunications -- 0.4% (continued)                                                         
    16,000          Metronet Communications, Expire 8/15/07 ....................  $     64,000 
     1,325          Primus Telecommunications Group, Expire 8/1/04 .............         6,625 
     1,300          RSL Communications Ltd., Expire 11/15/06 ...................        52,000 
       825          Versatel Telecommunication Warrants, Expire 5/15/08 ........         8,250 
     2,550          Wam!Net Inc., Expire 3/1/05 ................................        20,400 
                                                                                  ------------ 
                                                                                       572,275 
                                                                                  ------------ 
                    TOTAL WARRANTS                                                             
                    (Cost -- $436,901) .........................................       930,715 
                                                                                  ------------ 
<CAPTION>                                                                                      
  Face                                                                                         
 Amount                                Security                                          Value 
---------------------------------------------------------------------------------------------- 
<S>                 <C>                                                           <C> 
REPURCHASE AGREEMENTS -- 5.9%                                                                  
$9,000,000          Morgan Stanley, 5.380% due 10/1/98; Proceeds at maturity --                
                    $9,001,345; (Fully collateralized by various U.S. Treasury                 
                    securities; 3.625% to 12.750% due 8/15/03 to 4/15/28;                      
                    Market value -- $9,200,799)                                                
                    (Cost -- $9,000,000) .......................................     9,000,000 
                                                                                  ------------
                    TOTAL INVESTMENTS -- 100%                                                  
                    (Cost-- $156,606,724** )....................................  $152,123,283 
                                                                                  ============
</TABLE>

----------
+     Security is exempt from registration under Rule 144A of the Securities Act
      of 1933. This security may be resold in transactions that are exempt from
      registration, normally to qualified institutional buyers.
++    Represents local currency.
#     Non-income producing security.
**    Aggregate cost for Federal income tax purposes is substantially the same.

      See page 14 for definition of ratings.

                        See Notes to Financial Statement


                                       13
<PAGE>
 
[LOGO]                                                  Bond Ratings (unaudited)
================================================================================

All ratings are by Standard & Poor's Ratings Service ("Standard & Poor's"),
except those identified by an asterisk (*) are rated by Moody's Investors
Service, Inc. ("Moody's"). The definitions of the applicable rating symbols are
set forth below:

Standard & Poor's -- Ratings from "BBB" to "CCC" may be modified by the addition
of a plus (+) or minus (-) sign to show relative standings within the major
rating categories.

BBB               Bonds rated "BBB" are regarded as having an adequate
                  capacity to pay interest and repay principal. Whereas they
                  normally exhibit adequate protection parameters, adverse
                  economic conditions or changing circumstances are more likely
                  to lead to a weakened capacity to pay interest and repay
                  principal for bonds in this category than in higher rated
                  categories.

BB, B and CCC     Bonds rated BB, B and CCC are regarded, on balance, as
                  predominantly speculative with respect to the issuer's
                  capacity to pay interest and repay principal in accordance
                  with the terms of the obligation. BB indicates the lowest
                  degree of speculation and CCC the highest degree of
                  speculation. While such bonds will likely have some quality
                  and protective characteristics, these are outweighed by large
                  uncertainties or major risk exposures to adverse conditions.

Moody's -- Numerical modifiers 1, 2 and 3 may be applied to each generic rating
from "Ba" to "Caa," where 1 is the highest and 3 the lowest ranking within its
generic category.

Ba       --       Bonds rated "Ba" are judged to have  speculative  elements;
                  their future cannot be considered as well assured.  Often the
                  protection of interest and principal payments may be very
                  moderate and thereby not well safeguarded during both good and
                  bad times over the future. Uncertainty of position
                  characterizes bonds in this class.

B        --       Bonds rated "B" generally lack characteristics of desirable
                  investments. Assurance of interest and principal payments or
                  of maintenance of other terms of the contract over any long
                  period of time may be small.

Caa      --       Bonds rated "Caa" are of poor standing. Such issues may be in
                  default, or there may be present elements of danger may exist
                  with respect to principal or interest.

NR       --       Indicates that the bond is not rated by either Standard &
                  Poor's or Moody's.


                                       14
<PAGE>
 
[LOGO]                                      Statements of Assets and Liabilities
                                                  September 30, 1998 (unaudited)
================================================================================

<TABLE>
<S>                                                                          <C>
ASSETS:
   Investments, at value (Cost -- $156,606,724) ........                     $ 152,123,283
   Cash ................................................                               149
   Interest receivable .................................                         3,394,195
                                                                             -------------
Total Assets ...........................................                       155,517,627
                                                                             -------------
LIABILITIES:
   Bank loan (Note 7) ..................................                        30,000,000
   Payable for securities purchased ....................                           893,787
   Payable for open forward foreign
     currency contracts (Note 11) ......................                           184,730
   Investment advisory fees payable ....................                            94,073
   Administration fees payable .........................                            37,106
   Interest payable ....................................                            16,067
   Accrued expenses ....................................                           204,057
                                                                             -------------
   Total Liabilities ...................................                        31,429,820
                                                                             -------------
Total Net Assets .......................................                     $ 124,087,807
                                                                             =============

NET ASSETS:
   Par value of capital shares .........................                     $     154,359
   Capital paid in excess of par value .................                       128,783,306
   7.00% Cumulative Preferred Stock (Note 6) ...........                        30,000,000
   Overdistributed net investment income ...............                          (263,827)
   Accumulated net realized loss on security
     transactions ......................................                       (29,921,695)
   Net unrealized depreciation on investments and
     foreign currencies ................................                        (4,664,336)
                                                                             -------------
Total Net Assets .......................................                     $ 124,087,807
                                                                             =============

<CAPTION>
                                                                Per Share
                                                                ---------
<S>                                                              <C>         <C>
NET ASSET VALUE, COMPRISED OF:
7.00% Cumulative Preferred Stock redemption value ......        $ 1,000.00   $  30,000,000
Cumulative undeclared dividends on 7.00%
   Preferred Stock .....................................             20.81         624,241
                                                                ----------   -------------
Total allocated to Cumulative Preferred Stock ..........          1,020.81      30,624,241
                                                                ==========   -------------
Common Stock (15,435,845 shares outstanding) ...........        $     6.05      93,463,566
                                                                ==========   -------------
Total Net Assets .......................................                     $ 124,087,807
                                                                             =============
</TABLE>
                      See Notes to Financial Statements.


                                       15
<PAGE>
 
[LOGO]                                                   Statement of Operations
                                                        For the Six Months Ended
                                                  September 30, 1998 (unaudited)
================================================================================

<TABLE>
<CAPTION>
INVESTMENT INCOME:
<S>                                                                                <C>
   Interest ....................................................................   $  7,844,015
   Dividends ...................................................................        164,658
   Less: Interest expense (Note 7) .............................................       (918,317)
                                                                                   ------------
   Total Investment Income .....................................................      7,090,356
                                                                                   ------------
EXPENSES:
   Investment advisory fees (Note 2) ...........................................        408,333
   Administration fees (Note 2) ................................................        163,333
   Shareholder communications ..................................................         87,739
   Audit and legal .............................................................         48,424
   Directors' fees .............................................................         17,548
   Shareholder and system servicing fees .......................................         16,344
   Pricing .....................................................................         15,555
   Custody .....................................................................          3,609
   Other .......................................................................         20,807
                                                                                   ------------
   Total Expenses ..............................................................        781,692
                                                                                   ------------
Net Investment Income ..........................................................      6,308,664
                                                                                   ------------
REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS
AND FOREIGN CURRENCIES (NOTES 3 AND 11):
   Realized Gain (Loss) From:
     Security transactions (excluding short-term securities) ...................        439,646
     Foreign currency transactions .............................................        (42,927)
                                                                                   ------------
   Net Realized Gain ...........................................................        396,719
                                                                                   ------------
   Change in Net Unrealized Appreciation (Depreciation) of
   Investments and Foreign Currencies:
     Beginning of period .......................................................      9,425,614
     End of period .............................................................     (4,664,336)
                                                                                   ------------
   Increase in Net Unrealized Depreciation .....................................    (14,089,950)
                                                                                   ------------
Net Loss on Investments and Foreign Currencies .................................    (13,693,231)
                                                                                   ------------
Decrease in Net Assets From Operations .........................................   $ (7,384,567)
                                                                                   ============ 
</TABLE>

                      See Notes to Financial Statements.


                                       16
<PAGE>
 
[LOGO]                                       Statements of Changes in Net Assets
                                                        For the Six Months Ended
                                                  September 30, 1998 (unaudited)
                                               and the Year Ended March 31, 1998
================================================================================

<TABLE>
<CAPTION>
                                                                        September 30        March 31
                                                                       -------------    -------------
<S>                                                                    <C>              <C>
OPERATIONS:
   Net investment income ...........................................   $   6,308,664    $  12,914,504
   Net realized gain ...............................................         396,719        1,717,025
   Increase in net unrealized
     appreciation (depreciation) ...................................     (14,089,950)       6,555,506
                                                                       -------------    -------------
   Increase (Decrease) in Net Assets From Operations ...............      (7,384,567)      21,187,035
                                                                       -------------    -------------
DIVIDENDS PAID FROM NET INVESTMENT INCOME TO:
   7.00% Cumulative Preferred Stockholders .........................      (1,050,000)      (2,100,000)
   Common Stockholders .............................................      (5,552,215)     (11,728,952)
                                                                       -------------    -------------
   Decrease In Net Assets From
     Distributions To Shareholders .................................      (6,602,215)     (13,828,952)
                                                                       -------------    -------------
FUND SHARE TRANSACTIONS (Note 8):
   Net asset value of shares issued for
     reinvestment of dividends .....................................       1,592,190        3,448,238
                                                                       -------------    -------------
   Increase in Net Assets From
     Fund Share Transactions .......................................       1,592,190        3,448,238
                                                                       -------------    -------------
Increase (Decrease) in Net Assets ..................................     (12,394,592)      10,806,321
NET ASSETS:
   Beginning of period .............................................     136,482,399      125,676,078
                                                                       -------------    -------------
   End of period* ..................................................   $ 124,087,807    $ 136,482,399
                                                                       =============    =============
* Includes undistributed (overdistributed)
   net investment income of: .......................................   $    (263,827)   $      72,651
                                                                       =============    =============
</TABLE>

                      See Notes to Financial Statements.


                                       17
<PAGE>
 
[LOGO]                                                   Statement of Cash Flows
                                                        For the Six Months Ended
                                                   September 30,1998 (unaudited)
================================================================================

<TABLE>
<CAPTION>
<S>                                                                               <C>            <C>
NET INCREASE IN CASH:
Cash Flows Provided by Operating and Investing Activities:
  Interest and dividends received .............................................   $  6,892,830
  Operating expenses paid .....................................................       (740,080)
  Interest payments on bank loans .............................................       (993,942)
  Purchases of short-term securities, net .....................................     (2,691,000)
  Purchases of long-term securities ...........................................    (80,828,059)
  Proceeds from disposition of long-term securities ...........................     83,370,311
                                                                                  ------------
  Net Cash Provided By Operating and Investing Activities .....................                   $  5,010,060
                                                                                                  ------------
Cash Flows Used by Financing Activities:
  Cash dividends paid on 7.00% Cumulative Preferred Stock .....................     (1,050,000)
  Net Cash dividends paid on Common Stock* ....................................     (3,960,025)
                                                                                  ------------
  Net Cash Used By Financing Activities .......................................                   $ (5,010,025)
                                                                                                  ------------
Net Increase in Cash ..........................................................                             35
Cash--Beginning of Period .....................................................                            114
                                                                                                  ------------
Cash--End of Period ...........................................................                   $        149
                                                                                                  ============

RECONCILIATION OF INCREASE IN NET ASSETS FROM OPERATIONS TO NET CASH 
PROVIDED BY OPERATING AND INVESTING ACTIVITIES:
Decrease in Net Assets From Operations ........................................                   $ (7,384,567)
  Amortization of discount on securities ......................................     (1,226,382)
  Decrease in investments .....................................................     13,548,915
  Decrease in receivable for securities sold ..................................        217,091
  Increase in payable for securities purchased ................................       (258,907)
  Decrease in dividends and interest receivable ...............................        147,923
  Decrease in accrued expenses ................................................        (34,013)
                                                                                  ------------
  Total Adjustments ...........................................................                     12,394,627
                                                                                                  ------------
Net Cash Provided By Operating and Investing Activities .......................                   $  5,010,060
                                                                                                  ============
</TABLE>

*     Exclusive of dividend reinvestment of $1,592,190.

                       See Notes to Financial Statements.


                                       18
<PAGE>
 
[LOGO]                                             Notes to Financial Statements
                                                                     (unaudited)
================================================================================

      1. Significant Accounting Policies

      Zenix Income Fund Inc. ("Fund"), a Maryland corporation, is registered
under the Investment Company Act of 1940, as amended, as a diversified,
closed-end management investment company.

      The significant accounting policies followed by the Fund are: (a) security
transactions are accounted for on trade date; (b) securities traded in the
over-the-counter market, including listed securities for which the primary
market is believed to be over-the-counter, are valued at the mean between the
most recently quoted bid and ask prices provided by the principal market makers;
any security for which the primary market is an exchange is valued at the last
sale price on such exchange on the day of valuation or, if there was no sale on
such day, at the last bid price quoted. Securities and assets for which market
quotations are not readily available are valued at fair value as determined in
good faith by or under the direction of the Board of Directors of the Fund
including references to valuations of other securities which are considered
comparable in quality, interest rate and maturity; (c) securities maturing
within 60 days are valued at cost plus accreted discount, or minus amortized
premium, which approximates value; (d) the accounting records of the Fund are
maintained in U.S. dollars. All assets and liabilities denominated in foreign
currencies are translated into U.S. dollars based on the rate of exchange of
such currencies against U.S. dollars on the date of valuation. Purchases and
sales of securities, and income and expenses are translated at the rate of
exchange quoted on the respective date that such transactions are recorded.
Differences between income or expense amounts recorded and collected or paid are
adjusted when reported by the custodian bank; (e) dividend income is recorded on
the ex-dividend date and interest income is recorded on an accrual basis; (f)
gains or losses on the sale of securities are calculated by using the specific
identification method; (g) dividends and distributions to shareholders are
recorded monthly by the Fund on the ex-dividend date for the shareholders of
Common Stock based on net investment income. The holders of the 7.00% Cumulative
Preferred Stock shall be entitled to receive dividends when, as and if declared
by the Board of Directors of the Fund out of funds legally available to
shareholders at a rate of 7.00% per annum,


                                       19
<PAGE>
 
[LOGO]                                             Notes to Financial Statements
                                                         (unaudited) (continued)
================================================================================

payable semi-annually on June 15 and December 15; (h) the net asset value of the
Fund's Common Stock is determined no less frequently than the close of business
on the Fund's last business day of each week (generally Friday). It is
determined by dividing the value of the net assets available to Common Stock by
the total number of shares of Common Stock outstanding. For the purpose of
determining the net asset value per share of the Common Stock, the value of the
Fund's net assets shall be deemed to equal the value of the Fund's assets less
(1) the Fund's liabilities (including the outstanding principal amount on the
bank loan), (2) the aggregate liquidation value (i.e., $1,000 per outstanding
share) of the 7.00% Cumulative Redeemable Preferred Stock and (3) accumulated
and unpaid dividends on the outstanding Cumulative Redeemable Preferred Stock
issue; (i) the Fund intends to comply with the requirements of the Internal
Revenue Code of 1986, as amended, pertaining to regulated investment companies
and to make distributions of taxable income sufficient to relieve it from
substantially all Federal income and excise taxes; (j) the character of income
and gains to be distributed are determined in accordance with income tax
regulations which may differ from generally accepted accounting principles. At
March 31, 1998, reclassifications were made to the Fund's capital accounts to
reflect permanent book/tax differences and income and gains available for
distributions under income tax regulations. Net investment income, net realized
gains and net assets were not affected by this change; and (k) estimates and
assumptions are required to be made regarding assets, liabilities and changes in
net assets resulting from operations when financial statements are prepared.
Changes in the economic environment, financial markets and any other parameters
used in determining these estimates could cause actual results to differ.

      2. Advisory Agreement and Transactions with Affiliated Persons

      Mutual Management Corp. ("MMC"), a subsidiary of Salomon Smith Barney
Holdings Inc. ("SSBH"), acts as investment adviser to the Fund. The Fund pays
MMC a management fee calculated at an annual rate of 0.50% of the average daily
net assets (defined as the average daily value of the total assets of the Fund
less total liabilities other than the outstanding principal amount of the Bank
loan). This fee is calculated daily and paid monthly.


                                       20
<PAGE>
 
[LOGO]                                             Notes to Financial Statements
                                                         (unaudited) (continued)
================================================================================

      MMC also acts as the Fund's administrator for which the Fund pays a fee
calculated at an annual rate of 0.20% of the average daily net assets (defined
as the value of average daily net assets shall mean the average daily value of
the total assets of the Fund less liabilities other than the outstanding
principal amount of the Bank loan). This fee is calculated daily and paid
monthly.

      All officers and one Director of the Fund are employees of Salomon Smith
Barney Inc., another subsidiary of SSBH.

      3. Investments

      During the six months ended September 30, 1998, the aggregate cost of
purchases and proceeds from sales of investments (including maturities, but
excluding short-term securities) were as follows:

================================================================================
Purchases                                                            $80,569,152
--------------------------------------------------------------------------------
Sales                                                                 83,051,377
================================================================================

      At September 30, 1998, the aggregate gross unrealized appreciation and
depreciation of investments for Federal income tax purposes were substantially
as follows:

================================================================================
Gross unrealized appreciation                                       $ 3,615,200
Gross unrealized depreciation                                        (8,098,641)
--------------------------------------------------------------------------------
Net unrealized depreciation                                         $(4,483,441)
================================================================================

      4. Cash Flow Information

      The Fund invests in securities and distributes dividends from net
investment income and net realized gains. These activities are reported in the
Statements of Changes in Net Assets. Information on cash payments is presented
in the Statement of Cash Flows. Accounting practices that do not affect
reporting activities on a cash basis include unrealized gains or losses on
investment securities.

      5. Repurchase Agreements

      The Fund purchases (and its custodian takes possession of) U.S. government
securities from banks and securities dealers subject to


                                       21
<PAGE>
 
[LOGO]                                             Notes to Financial Statements
                                                         (unaudited) (continued)
================================================================================

agreements to resell the securities to the sellers at a future date (generally,
the next business day) at an agreed upon higher repurchase price. The Fund
requires continual maintenance of the market value of the collateral in amounts
at least equal to the repurchase price.

      6. Cumulative Redeemable Preferred Stock

      On March 16, 1993, the Fund issued 30,000 shares of 7.00% Cumulative
Preferred Stock, which will be redeemed in full on April 15, 2000, at a price
equal to $1,000 per share, plus accumulated and unpaid dividends. At September
30, 1998, 220,000 authorized shares of 7.00% Cumulative Preferred Stock with a
par value of $0.01 remained unissued. Cumulative undeclared dividends on the
outstanding Preferred Stock amounted to $624,241 at September 30, 1998.

      Moody's Investors Service, Inc. and Standard & Poor's Ratings Service have
reconfirmed their respective Aa3 and AA+ ratings of the Fund's 7% Cumulative
Preferred Stock.

      7. Bank Loan

      The Fund has a $30,000,000 line of credit with PNC Bank, N.A. Interest on
the loan can be paid based on 30-, 60- or 90-day periods as elected by the Fund.
The interest on the loan is currently calculated at the federal-funds rate plus
40 basis points. The line of credit expires on July 31, 2008. Interest expense
related to the loan for the six months ended September 30, 1998 was $918,317.

      8. Common Stock

      At September 30, 1998, the Fund had 250,000,000 shares of common stock
authorized with a par value of $0.01 per share.

     Common stock transactions were as follows:

                                 Six Months Ended                Year Ended
                                September 30, 1998             March 31, 1998
                               ---------------------       ---------------------
                               Shares       Amount         Shares       Amount
================================================================================
Shares issued on
   reinvestment                233,726    $1,592,190       460,479    $3,448,238
================================================================================


                                       22
<PAGE>
 
[LOGO]                                             Notes to Financial Statements
                                                         (unaudited) (continued)
================================================================================

      9. Capital Loss Carryforward

      At March 31, 1998, the Fund had, for Federal income tax purposes, capital
loss carryforwards of approximately $29,966,000 available to offset future
realized capital gains, if any. To the extent that these carryforward losses are
used to offset capital gains, it is probable that the gains so offset will not
be distributed.

      The amount and expiration of the carryforwards are indicated below.
Expiration occurs on March 31 of the year indicated:

                             1999           2000          2003           2004
================================================================================
Carryforward Amounts      $14,407,000    $8,395,000    $4,873,000     $2,291,000
================================================================================

      10. Asset Maintenance Requirement

      The Fund is required to maintain certain asset coverages with respect to
the Cumulative Preferred Stock (of at least 200%). If the Fund fails to maintain
these requirements as of the last business day of the month and does not cure
such failure by the last business day of the following month, the Fund is
required to redeem certain of the Cumulative Preferred Stock in order to meet
these requirements. Additionally, failure to meet the foregoing asset
requirements would restrict the Fund's ability to pay dividends.

      11. Forward Foreign Currency Contracts

      At September 30, 1998, the Fund had open forward foreign currency
contracts as described below. The Fund bears the market risk that arises from
changes in foreign currency exchange rates. The unrealized loss on the contracts
is reflected as follows:

                                    Local       Market   Settlement  Unrealized
Foreign Currency                   Currency       Value     Date        Loss
================================================================================
To Sell:
British Pound                      280,906   $  473,528   2/25/99    $  (18,460)
European Currency Unit             676,312      798,064   11/30/98      (43,042)
German Mark                      2,563,158    1,538,631   12/3/98       (66,668)
German Mark                      1,499,025      902,320   1/28/99       (56,560)
--------------------------------------------------------------------------------
Total Unrealized Loss on Open Forward
   Foreign Currency Contracts                                         $(184,730)
================================================================================


                                       23
<PAGE>
 
[LOGO]                                                   Financial Highlights
================================================================================

Contained below is per share operating performance data for a share of common
stock outstanding, total return and ratios to average net assets based on Common
Shares outstanding. This information has been derived from information provided
in the financial statements and market price data for the Fund's shares.

For a share of common stock outstanding throughout each year ended March 31,
except where noted:

<TABLE>
<CAPTION>
                                                         1998(1)           1998            1997
                                                      -----------      -----------     -----------
<S>                                                   <C>              <C>             <C>        
Net Asset Value, Beginning of Period ..............   $      6.96      $      6.45     $      6.31
                                                      -----------      -----------     -----------
Income From Operations:
   Net investment income ..........................          0.41             0.87            0.92
   Net realized and unrealized gain (loss) ........         (0.89)            0.56            0.08
                                                      -----------      -----------     -----------
   Total Income (Loss) From Operations ............         (0.48)            1.43            1.00
                                                      -----------      -----------     -----------
Distributions:
   Dividends declared to 7.00% Cumulative Preferred
     Stockholders .................................         (0.07)           (0.14)          (0.14)
   Dividends paid from net investment income ......         (0.36)           (0.78)          (0.72)
   Change in accumulated undeclared dividends
     on Preferred Stock ...........................            --               --              --
                                                      -----------      -----------     -----------
   Total Distributions ............................         (0.43)           (0.92)          (0.86)
                                                      -----------      -----------     -----------
Net Asset Value, End of Period ....................   $      6.05      $      6.96     $      6.45
                                                      ===========      ===========     ===========
Market Value, End of Period .......................   $      6.31      $      7.50     $      7.25
                                                      ===========      ===========     ===========
Total Return, Based on Market Value* ..............        (11.24)%++        14.81%          15.55%
                                                      ===========      ===========     ===========
Total Return, Based on Net Asset Value* ...........         (8.34)%++        19.75%          14.04%
                                                      ===========      ===========     ===========
Net Assets**, End of Period (000's) ...............   $    93,464      $   105,861     $    95,034
                                                      ===========      ===========     ===========
Ratios to Average Net Assets Based on
Common Shares Outstanding***:
   Net Investment Income ..........................         12.24%+          12.60%          14.35%
   Interest Expense ...............................          1.78+            1.81            1.92
   Other Expenses .................................          1.52+            1.51            1.59

Portfolio Turnover Rate ...........................            52%              79%            101%
</TABLE>

----------
(1)   For the six months ended September 30, 1998 (unaudited).
*     The total return calculation assumes that dividends are reinvested in
      accordance with the Fund's dividend reinvestment plan.
**    Exclusive of preferred shares outstanding.
***   Calculated on basis of average net assets of common shareholders. Ratios
      do not reflect the effect of dividend payments to preferred shareholders.
      The amounts for 1998 and 1997 have been recalculated to reflect this
      methodology.
++    Total return is not annualized, as it may not be representative of the
      total return for the year.
+     Annualized.


                                       24
<PAGE>
 
[LOGO]                                          Financial Highlights (continued)
================================================================================

For a share of common outstanding throughout each year ended March 31:
<TABLE>
<CAPTION>
                                                          1996             1995            1994#
                                                      -----------      -----------     -----------
<S>                                                   <C>              <C>             <C>
Net Asset Value, Beginning of Year ................   $      5.88      $      6.76     $      6.86
                                                      -----------      -----------     -----------
Income From Operations:
   Net investment income ..........................          0.86             0.93            1.02
   Net realized and unrealized gain (loss) ........          0.45            (0.78)          (0.13)
                                                      -----------      -----------     -----------
   Total Income From Operations ...................          1.31             0.15            0.89
                                                      -----------      -----------     -----------
Distributions:
   Dividends declared to 7.00% Cumulative Preferred
     Stockholders .................................         (0.15)           (0.16)          (0.11)
   Dividends declared to 9.67% Cumulative Preferred
     Stockholders .................................            --               --           (0.12)
   Dividends paid from net investment income ......         (0.73)           (0.87)          (0.82)
   Change in accumulated undeclared dividends on
     Preferred Stock ..............................            --               --            0.06
                                                      -----------      -----------     -----------
   Total Distributions ............................         (0.88)           (1.03)          (0.99)
                                                      -----------      -----------     -----------
Net Asset Value, End of Year ......................   $      6.31      $      5.88     $      6.76
                                                      ===========      ===========     ===========
Market Value, End of Year .........................   $      7.00      $      6.63     $      7.13
                                                      ===========      ===========     ===========
Total Return, Based on Market Value* ..............         18.35%            6.41%          10.02%
                                                      ===========      ===========     ===========
Total Return, Based on Net Asset Value* ...........         20.01%           (0.53)%         10.24%
                                                      ===========      ===========     ===========
Net Assets**, End of Year (000's) .................   $    90,318      $    80,309     $    87,726
                                                      ===========      ===========     ===========
Ratios to Average Net Assets Based on
Common Shares Outstanding***:
   Net Investment Income ..........................         14.21%           15.35%          14.38%
   Interest Expense ...............................          1.98             1.58            0.92
   Other Expenses .................................          1.65             1.65            1.60
Portfolio Turnover Rate ...........................            87%              79%            102%
</TABLE>

----------
#     Per share amounts have been calculated using the monthly average shares
      method, rather than the undistributed net investment income method,
      because it more accurately reflects the per share data for the period.
*     The total return calculation assumes that dividends are reinvested in
      accordance with the Fund's dividend reinvestment plan.
**    Exclusive of preferred shares outstanding.
***   Calculated on basis of average net assets of common shareholders. Ratios
      do not reflect the effect of dividend payments to preferred shareholders.
      The amount for 1996 has been recalculated to reflect this methodology.
      

                                       25
<PAGE>
 
[LOGO]                                   Other Financial Information (unaudited)
================================================================================

     The table below sets out information with respect to Cumulative Preferred
Stock, Senior Money Market Notes and Bank Credit Facility:

<TABLE>
<CAPTION>
                                            1998(1)     1998        1997      1996       1995       1994
                                          ---------   --------   --------   --------   --------  --------
<S>                                       <C>        <C>        <C>        <C>        <C>        <C>
7.00% Cumulative Preferred Stock (2)
  Total amount outstanding (000s)         $ 30,000   $ 30,000   $ 30,000   $ 30,000   $ 30,000   $ 30,000
  Asset Coverage Per Share                   2,558      2,760      2,580      2,490      2,439      2,583
  Involuntary Liquidating Preference
    Per Share (3)                            1,000      1,000      1,000      1,000      1,000      1,000
  Average Market Value Per Share (3)(4)      1,000      1,000      1,000      1,000      1,000      1,000
Senior Money Market Notes
  Total amount outstanding (000s)               --         --         --         --     25,800     25,800
  Asset Coverage (000s)                         --         --         --         --    135,966    143,946
PNC Bank Credit Facility
  Total amount outstanding (000s)           30,000     30,000     30,000     30,000         --         --
  Asset Coverage (000s)                    153,500    165,900    154,800    149,400         --         --
</TABLE>

----------
(1)   As of September 30, 1998.
(2)   Redeemable April 15, 2000.
(3)   Excludes accrued interest or accumulated undeclared dividends.
(4)   See Note 6.


                                       26
<PAGE>
 
[LOGO]                               Quarterly Results of Operations (unaudited)
================================================================================

<TABLE>
<CAPTION> 
                                                                                                  Net Increase
                                                                        Net Realized               (Decrease)
                                                                       and Unrealized             in Net Assets
                         Investment            Net Investment           Gain (Loss)                    From
                           Income                  Income              on Investments               Operations
                     ---------------------   -------------------   -----------------------    ---------------------
                                     Per                   Per                      Per                       Per
Quarter Ended             Total     Share*     Total      Share*       Total       Share*       Total        Share*
-------------        ------------   ------   ----------   ------   -------------   -------    -----------    ------
<S>                    <C>          <C>      <C>          <C>      <C>             <C>        <C>            <C>
June 30, 1996          $4,102,702   $0.29    $3,322,425   $0.23    $ (1,014,235)   $(0.07)    $ 2,308,190    $ 0.16
September 30, 1996      4,224,470    0.29     3,370,554    0.23       2,772,544      0.19       6,143,098      0.42
December 31, 1996       4,132,306    0.28     3,304,424    0.22       1,557,018      0.11       4,861,442      0.33
March 31, 1997          4,132,818    0.28     3,335,373    0.23      (2,167,250)    (0.15)      1,168,123      0.08
June 30, 1997           3,810,798    0.26     3,442,440    0.23       4,087,876      0.29       7,530,316      0.52
September 30, 1997      3,652,220    0.24     3,266,777    0.22       4,374,410      0.29       7,641,187      0.51
December 31, 1997       3,786,388    0.25     3,387,528    0.23      (1,501,241)    (0.10)      1,886,287      0.13
March 31, 1998          3,209,147    0.22     2,817,759    0.19       1,311,486      0.08       4,129,245      0.27
June 30, 1998           3,578,838    0.23     3,185,558    0.21      (1,919,184)    (0.13)      1,266,374      0.08
September 30, 1998      3,511,518    0.23     3,123,106    0.20     (11,774,047)    (0.76)     (8,650,941)    (0.56)
</TABLE>

----------
*  Per share of Common Stock.


                                       27
<PAGE>
 
[LOGO]                                                Financial Data (unaudited)
================================================================================

For a share of common stock outstanding throughout each period:
                                                                      Dividend
      Record       Payable       NYSE       Net Asset   Dividend    Reinvestment
       Date         Date     Closing Price   Value*       Paid          Price
================================================================================
      7/23/96      7/26/96      $6.875       $6.22        $0.060        $6.531
      8/27/96      8/30/96       6.875        6.29         0.060         6.531
      9/24/96      9/27/96       7.125        6.37         0.060         6.769
     10/22/96     10/25/96       7.125        6.40         0.060         6.769
     11/25/96     11/29/96       7.125        6.47         0.060         6.769
     12/23/96     12/27/96       7.125        6.53         0.061         6.769
      1/28/97      1/31/97       7.250        6.62         0.061         6.888
      2/25/97      2/28/97       7.375        6.73         0.061         7.006
      3/24/97      3/27/97       7.125        6.51         0.061         6.769
      4/22/97      4/25/97       7.125        6.38         0.061         6.769
      5/27/97      5/30/97       7.500        6.59         0.061         7.125
      6/24/97      6/27/97       7.625        6.77         0.061         7.244
      7/22/97      7/25/97       7.750        6.81         0.061         7.363
      8/26/97      8/29/97       7.938        6.88         0.061         7.541
      9/23/97      9/26/97       7.938        7.01         0.063         7.541
     10/28/97     10/31/97       8.000        6.93         0.063         7.600
     11/24/97     11/28/97       8.190        6.91         0.063         7.778
     12/22/97     12/26/97       8.250        6.93         0.063         7.838
     12/31/97      1/2/98        8.250        6.91         0.040         7.838
      1/27/98      1/30/98       8.063        6.90         0.063         7.659
      2/24/98      2/27/98       8.500        6.95         0.063         8.075
      3/24/98      3/27/98       7.688        6.95         0.061         7.303
      4/21/98      4/24/98       7.500        6.95         0.061         7.125
      5/26/98      5/29/98       7.500        6.89         0.061         7.125
      6/23/98      6/26/98       7.625        6.82         0.061         7.244
      7/28/98      7/31/98       7.438        6.85         0.061         7.066
      8/25/98      8/28/98       6.563        6.54         0.061         6.409
      9/22/98      9/25/98       6.375        6.02         0.058         6.056
================================================================================
*  As of record date


                                       28
<PAGE>
 
[LOGO]                                                Dividend Reinvestment Plan
                                                                     (unaudited)
================================================================================

      Under the Fund's Dividend Reinvestment Plan ("Plan"), a shareholder whose
Common Stock is registered in his own name will have all distributions
reinvested automatically by First Data Investor Services Group, Inc. ("First
Data"), as purchasing agent under the Plan, unless the shareholder elects to
receive cash. Distributions with respect to shares registered in the name of a
broker-dealer or other nominee (that is, in "street name") will be reinvested by
the broker or nominee in additional Common Stock under the Plan, but only if the
service is provided by the broker or nominee, and the broker or nominee makes an
election on behalf of the shareholder to participate in the Plan. A shareholder
who holds Common Stock registered in the name of a broker or other nominee may
not be able to transfer the Common Stock to another broker or nominee and
continue to participate in the Plan. Investors who own Common Stock registered
in street name should consult their broker-dealers for details regarding
reinvestment. All distributions to shareholders who do not participate in the
Plan will be paid by check mailed directly to the record holder by or under the
direction of First Data, as dividend-paying agent.

      The number of shares of Common Stock distributed to participants in the
Plan in lieu of a cash dividend is determined in the following manner. Whenever
the market price of the Common Stock is equal to or exceeds 98% of net asset
value per share on the date of valuation, participants will be issued shares of
Common Stock valued at the greater of (i) 98% of net asset value per share or
(ii) 95% of the market price. To the extent that the Fund issues shares to
participants in the Plan at a discount to net asset value, the interests of
remaining shareholders (i.e., those who do not participate in the Plan) in the
Fund's net assets will be proportionately diluted.

      If 98% of the net asset value per share of the Common Stock at the time of
valuation exceeds the market price of the Common Stock, or if the Fund declares
a dividend or capital gains distribution payable only in cash, First Data will
buy Common Stock on the open market, on the New York Stock Exchange or
elsewhere, for the participants' accounts. If, following the commencement of the
purchases and before First Data has completed its purchases, the market price
exceeds 98% of the net asset value per share of


                                       29
<PAGE>
 
[LOGO]                                                Dividend Reinvestment Plan
                                                         (unaudited) (continued)
================================================================================

the Common Stock, First Data will attempt to terminate purchases in the open
market and cause the Fund to issue the remaining portion of the dividend or
distribution by issuing shares at a price equal to 98% of the net asset value
per share. In this case, the number of shares of Common Stock received by a Plan
participant will be based on the weighted average prices paid for shares
purchased in the open market and the price at which the Fund issues the
remaining shares. To the extent First Data is unable to stop open market
purchases and cause the Fund to issue the remaining shares, the average per
share paid by First Data may exceed 98% of the net asset value per share of the
Common Stock, resulting in the acquisition of fewer shares in Common Stock
issued by the Fund at 98% of net asset value per share. First Data will begin to
purchase Common Stock on the open market as soon as a practicable after the
payment date of the dividend or capital gains distribution, but in no event
shall such purchases continue later than 30 days after that date except when
necessary to comply with applicable provisions of the Federal securities law.

      First Data maintains all shareholder accounts in the Plan and furnishes
written confirmations of all transactions in each account, including information
needed by a shareholder for personal and tax records. The automatic reinvestment
of dividends and capital gains distributions will not relieve Plan participants
of any income tax that may be payable on the dividends or capital gains
distributions. Common Stock in the account of each Plan participant will be held
by First Data in uncertificated form in the name of the Plan participant.

      Plan participants are not subject to any charge for reinvesting dividends
or capital gains distributions. Each Plan participant will, however, bear a
proportionate share of brokerage commissions incurred with respect to First
Data's open market purchases of shares of Common Stock in connection with the
reinvestment of dividends or capital gains distributions. For the year ended
March 31, 1998, no such brokerage commissions were incurred.

      A shareholder may terminate participation in the Plan at any time by
notifying First Data in writing. A termination will be effective immediately if
notice is received by First Data not less than 10 days before any dividend or
distribution record date. Otherwise, the termination will be effective, and only


                                       30
<PAGE>
 
[LOGO]                                                Dividend Reinvestment Plan
                                                         (unaudited) (continued)
================================================================================

with respect to any subsequent dividends or distributions, on the first trading
day after the dividend or distribution has been credited to the participant's
account in additional shares of Common Stock of the Fund. Upon termination
according to a participant's instructions, First Data will either (a) issue
certificates for the whole shares credited to a Plan account and a check
representing any fractional shares or (b) sell the shares in the market. There
will be a $5.00 fee assessed for liquidation service, plus brokerage
commissions, and First Data is authorized to sell a sufficient number of a
participant's shares to cover such amounts.

      Experience under the Plan may indicate that changes to it are desirable.
The Fund reserves the right to amend or terminate the Plan as applied to any
dividend or capital gains distributions paid subsequent to written notice of the
change sent to participants at least 30 days before the record date for the
dividend or capital gains distribution. The Plan also may be amended or
terminated by First Data or the Fund at least 30 days' written notice to Plan
participants. All correspondence concerning the Plan should be directed by mail
to First Data Investor Services Group, Inc., P.O. Box 8030, Boston,
Massachusetts 02266-8030 or by telephone at 1-800-331-1710.

                   -----------------------------------------

      Notice is hereby given in accordance with Section 23(c) of the Investment
Company Act of 1940, as amended, that from time to time the Fund may purchase
shares of its common stock in the open market.


                                       31
<PAGE>
 
                      [This page intentionally left blank]
<PAGE>
 
DIRECTORS

Allan J. Bloostein
Martin Brody
Dwight B. Crane
Robert A. Frankel
William R. Hutchinson
Heath B. McLendon

Charles F. Barber, Emeritus

OFFICERS

Heath B. McLendon
Chairman of the Board
Lewis E. Daidone
Senior Vice President
and Treasurer
John C. Bianchi
Vice President and
Investment Officer
Thomas M. Reynolds
Controller
Christina T. Sydor
Secretary

            This report is intended only for the shareholders of the
                             ZENIX Income Fund Inc.
               It is not a Prospectus, circular or representation
              intended for use in the purchase or sale of shares of
               the Fund or any securities mentioned in the report.

                                  FD01206 11/98