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


                                     [LOGO]


                                                                Quarterly Report
                                                                   June 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 first quarter report for the Zenix
Income Fund Inc. ("Fund") for the three month period ended June 30, 1998. Over
the past three months the Fund paid income dividends totaling $0.18 per share.
The table below shows the annualized distribution rate and three-month total
return for the Fund based on its June 30, 1998 net asset value ("NAV") per share
and its New York Stock Exchange ("NYSE") closing share price.

<TABLE>
<CAPTION>
                                         Annualized                Three-Month
           Price Per Share            Distribution Rate            Total Return
           ---------------            -----------------            ------------
<S>                                          <C>                       <C>  
           $6.83 (NAV)                       10.72%                    0.66%
           $7.63 (NYSE)                       9.59%                    4.35%
</TABLE>

The Fund's performance compares favorably with the three-month average total
return of 0.21% based on NAV for closed-end high yield bond funds as reported by
Lipper Analytical Services, Inc. (Lipper is an independent mutual
fund-perfomance tracking organization).

We believe we've been able to generate consistent performance returns in the
Fund through prudent asset selection with a heavy focus on high yield bonds
issued by companies with improving fundamentals.


                                       1

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Market and Economic Overview

The high yield bond market generated relatively weak results in the second
quarter of 1998 and underperformed most other sectors of the bond market. The
30-year U.S. Treasury bond generated the strongest results of all the sectors
(e.g., a total return of more than 6%), as many investors became more convinced
that the Asian crisis would contribute to an economic slowdown in the U.S.
beginning in the second quarter of 1998. The U.S. Treasury market has been
sought out as a "safe haven" by many investors concerned about increased
economic uncertainty. Moreover, an extremely heavy amount of new high yield bond
issuance also caused the high yield bond market to underperform other U.S. bond
market sectors. The higher-rated issues generated the strongest results among
high yield bonds given their greater sensitivity to interest rates. On the other
hand, the lowest-rated high yield bond issues generated the weakest returns and
that was not surprising given their greater sensitivity to general economic
conditions and stock market performance. While the stock market generated
positive results during the reporting period, there was considerably greater
volatility in the stock markets because of the higher uncertainty among many
investors.

Year to date the total of newly issued high yield bonds was roughly $110
billion, which is more than twice last year's figure of about $50 billion.
Moreover, year-to-date approximately $15 billion of cash inflows has gone into
high yield bond mutual funds, while above last year's total of $8 billion, the
current year's inflows were clearly insufficient to counterbalance the effects
of the extremely heavy new issue calendar. However, continued strong demand for
high yield bonds from pension funds and insurance companies somewhat limited the
underperformance of the high yield bond market versus other bond sectors during
the second quarter of 1998.

The U.S. economy today remains generally supportive of high yield bonds and
inflation continues to be modest. In fact, recent retail sales growth and U.S.
housing sales and employment remain quite strong. We believe that it's still an
open question whether Asia's problems will have any meaningful negative impact
on future U.S. economic growth. While the Fed remains concerned about the
strength of the U.S. economy and the potential for higher inflation in the
future, there has been little evidence of inflationary pressures so far.


                                       2

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Portfolio Strategy and Market Outlook

The Fund is cautiously positioned with a heavy emphasis in better quality,
intermediate maturity "B" and "BB" rated high yield bonds. As of June 30, 1998,
the Fund's average maturity on a call-adjusted basis was approximately 6.5
years. (Average maturity on a call-adjusted basis takes into account that the
Fund's maturity is calculated based on the underlying bonds' call dates rather
than their stated maturity.) In addition, the Fund continued to emphasize
telecommunications issues as well as cable and media issues.

As the high yield bond market continued to underperform during the second
quarter of 1998, we began to gradually 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 over the past six months. (Deflation is when prices actually
fall. Deflation should not be confused with disinflation. Disinflation is the
slowing down of the rate at which prices increase.) We have recently started to
lower our exposure to the energy industry given the continued weakness in energy
prices and our expectation that as long as Asia remains mired in difficulties,
energy prices should remain depressed. Yet we remain positive on the long-term
trends in the energy industry and do not plan to entirely eliminate the Fund's
current energy positions.

Many other high-yield bond funds continue to be aggressively invested in
lower-quality high yield bonds in an effort to maintain their dividend yields
and to generate competitive performance. As a result of the recent correction in
the world's stock markets, these more speculative high yield bond issues have
started to perform poorly during the past six months. Given their more
speculative features, lower-quality high yield bonds tend to correlate more
closely to the performance of broad stock markets than other kinds of bonds. In
addition, many high yield bond funds have continued to invest in emerging market
government bonds, common stocks, convertible securities and derivatives, all of
which have suffered varying degrees of corrections. Although the Fund is also
affected by market and economic conditions, we believe our commitment to owning
better quality high yield bonds should make the Fund less vulnerable to higher
stock market volatility.

While we still expect U.S. economic growth to slow and corporate profit margins
may deteriorate for the rest of 1998, we do not anticipate any meaningful U.S.
economic slowdown for the balance of the year. As a result, we have become more
opportunistically invested in select better-priced "B" and "BB" rated new
issues.


                                       3

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<PAGE>
 
--------------------------------------------------------------------------------

In closing, thank you for investing in the Zenix Income Fund. We look forward to
continuing to help you achieve 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

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


July 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>
 
<TABLE>
<CAPTION>

[LOGO]

                                                                              Schedule of Investments
                                                                            June 30, 1998 (unaudited)
=====================================================================================================
   Face
  Amount       Ratings                        Security                                     Value
-----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                            <C>
CORPORATE BONDS AND NOTES -- 93.3%
Aerospace/Defense -- 2.2%
$ 2,500,000   Ba2*   Airplanes Pass Through Trust, Corporate Collateralized
                       Mortgage Obligation, 10.875% due 3/15/19 ................    $    2,823,850
    650,000   BB     Morgan Stanley Aircraft Finance, Corporate
                       Collateralized Mortgage Obligation, 8.700% due 3/15/23 ..           653,250
                                                                                    --------------
                                                                                         3,477,100
                                                                                    --------------
Banking -- 2.1%
                     First Nationwide Parent Holdings Ltd.:
  2,675,000   Ba3*     Sr. Notes, 12.500% due 4/15/03 ..........................         3,062,875
    250,000   Ba2*     Sr. Sub. Notes, 10.625% due 10/1/03 .....................           283,750
                                                                                    --------------
                                                                                         3,346,625
                                                                                    --------------
Broadcasting/Cable -- 12.6%
                     Century Communications Corp.:
    350,000   BB-      Sr. Discount Notes, zero coupon bond to yield
                        8.160% due 3/15/03 .....................................           238,000
    925,000   BB-      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 ....................................         1,252,500
                     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 .....................................         1,173,750
    550,000   BB-      9.875% due 4/1/23 .......................................           611,875
  2,000,000   B      Marcus Cable Co. LP, Sr. Debentures,
                       11.875% due 10/1/05 .....................................         2,145,000
                     Rogers Cablesystems of America, Inc.:
    850,000   BB+      Sr. Notes, Series B, 10.000% due 3/15/05 ................           943,500
  1,000,000   BB+      Sr. Sub. Debentures, 10.000% due 12/1/07 ................         1,112,500
  2,100,000   BB-      Sr. Sub. Debentures, 11.000% due 12/1/15 ................         2,462,250
    400,000   BB-    Rogers Communications Inc., Sr. Notes,
                       8.875% due 7/15/07 ......................................           402,000
                     TV Azteca SA, Guaranteed Sr. Notes:
    525,000   Ba3*     Series A, 10.125% due 2/15/04 ...........................           526,312
    950,000   Ba3*     Series B, 10.500% due 2/15/07 ...........................           954,750
  5,300,000   B      United International Holdings Inc., Sr. Discount Notes,
                       step bond to yield 10.714% due 2/15/08+ .................         3,272,750
  1,000,000   BBB-   Videotron Group Ltd., Sr. Notes, 10.625% due 2/15/05 ......         1,120,000
                                                                                    --------------
                                                                                        20,497,937
                                                                                    --------------
</TABLE>

                       See Notes to Financial Statements.

                                       6
<PAGE>
 
<TABLE>
<CAPTION>

[LOGO]

                                                                  Schedule of Investments (continued)
                                                                            June 30, 1998 (unaudited)
=====================================================================================================
   Face
  Amount       Ratings                        Security                                     Value
-----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                            <C>
Chemicals -- 1.4%
$ 1,000,000   B1*    NL Industries Inc., Sr. Secured Notes,
                       11.750% due 10/15/03 ....................................    $    1,107,500
  1,150,000   B      Unifrax Investment Corp., Sr. Notes, 10.500% due 11/1/03 ..         1,204,625
                                                                                    --------------
                                                                                         2,312,125
                                                                                    --------------
Consumer Durables -- 0.7%
  1,100,000   B      Outboard Marine Corp., Sr. Notes, 10.750% due 6/1/08 ......         1,135,750
                                                                                    --------------
Diversified Manufacturing -- 2.3%
    500,000   B-     Alvey Systems Inc., Sr. Sub. Notes, 11.375% due 1/31/03 ...           522,500
    450,000   B-     Eagle-Picher Industrial Inc., Sr. Sub. Notes,
                       9.375% due 3/1/08 .......................................           458,438
    950,000   B3*    Interlake Corp., Sr. Sub. Debentures, 12.125% due 3/1/02 ..           978,500
  1,000,000   B2*    Intertek Finance PLC, Sr. Sub. Notes,
                       Series B, 10.250% due 11/1/06 ...........................         1,062,500
    700,000   B+     Park-Ohio Industries, Sr. Sub. Notes, 9.250% due 12/1/07 ..           715,750
                                                                                    --------------
                                                                                         3,737,688
                                                                                    --------------
Diversified Services -- 0.7%
    650,000   NR     Axiohm Transaction Solutions, Sr. Sub. Notes,
                       9.750% due 10/1/07 ......................................           656,500
    500,000   B-     Outsourcing Solutions, Sr. Sub. Notes, 11.000% due 11/1/06            543,750
                                                                                    --------------
                                                                                         1,200,250
                                                                                    --------------
Electric Utilities -- 4.0%
  2,350,000   Ba1*   AES Corp., Sr. Sub. Notes, 8.500% due 11/1/07 .............         2,388,187
                     Calpine Corp., Sr. Notes:
  1,350,000   Ba2*     10.500% due 5/15/06 .....................................         1,481,625
    750,000   Ba2*     8.750% due 7/15/07 ......................................           770,625
    891,853   BB     Midland Cogeneration Venture Limited Partnership,
                       Midland Funding, Sr. Secured Lease Obligation
                       Bond, Series C, 10.330% due 7/23/02 .....................           958,742 
                     Niagara Mohawk Power:
    350,000   BB-      Sr. Notes, Series G, 7.750% due 10/1/08 .................           359,625
    775,000   BB-      Step bond to yield 8.376% due 7/1/10 ....................           538,625
                                                                                    --------------
                                                                                         6,497,429
                                                                                    --------------
Electronics-Computers -- 6.2%
  1,000,000   B      Celestica International Inc., Sr. Sub. Notes,
                       10.500% due 12/31/06 ....................................         1,103,750
</TABLE>

                       See Notes to Financial Statements.

                                       7
<PAGE>
 
<TABLE>
<CAPTION>

[LOGO]

                                                                  Schedule of Investments (continued)
                                                                            June 30, 1998 (unaudited)
=====================================================================================================
   Face
  Amount       Ratings                        Security                                     Value
-----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                            <C>
Electronics-Computers --  6.2% (continued)
$ 1,500,000   B      Fairchild Semiconductor Inc., Sr. Sub. Notes,
                        10.125% due 3/15/07 ....................................    $    1,548,750
  1,000,000   B-     Graphic Controls Corp., Sr. Sub. Notes, 12.000% due 9/15/05         1,121,250
                     Unisys Corp., Sr. Notes:
  1,800,000   Ba3*     12.000% due 4/15/03 .....................................         2,045,250
  2,325,000   Ba3*     11.750% due 10/15/04 ....................................         2,697,000
  1,200,000   B-     Viasystems Inc., Sr. Sub. Notes, 9.750% due 6/1/07 ........         1,179,000
    600,000   NR     Wam!Net Inc., step bond to yield 13.250% due 3/1/05 .......           378,750
                                                                                    --------------
                                                                                        10,073,750
                                                                                    --------------
Finance -- 3.5%
  1,500,000   B      Amresco Inc., Sr. Sub. Notes, Series A, 10.000% due 3/15/04         1,558,125
  1,000,000   B2*    Ocwen Capital Trust, Guaranteed Notes, 10.875% due 8/1/27 .         1,092,500
  2,750,000   BB-    Ocwen Financial Corp., Notes, 11.875% due 10/1/03 .........         3,093,750
                                                                                    --------------
                                                                                         5,744,375
                                                                                    --------------
Foods -- 2.4%
    850,000   B-     B&G Foods Inc., Sr. Sub. Notes, 9.625% due 8/1/07 .........           864,875
  1,325,000   B      Imperial Holly Corp., Sr. Sub. Notes, 9.750% due 12/15/07 .         1,338,250
  1,500,000   B2*    Van De Kamp Inc., Sr. Sub. Notes, 12.000% due 9/15/05 .....         1,678,125
                                                                                    --------------
                                                                                         3,881,250
                                                                                    --------------
Health Care/Drugs/Hospital Supplies -- 6.6%
  1,600,000   BB     ICN Pharmaceutical Inc., Sr. Notes, 9.250% due 8/15/05 ....         1,700,000
                     Integrated Health Services Inc., Sr. Sub. Notes:
    715,000   B2*      9.500% due 9/15/07 ......................................           750,750
  1,400,000   B2*      9.250% due 1/15/08 ......................................         1,454,250
  2,700,000   B-     Magellan Health Services Inc., Sr. Sub. Notes,
                        9.000% due 2/15/08+ ....................................         2,679,750
    900,000   B-     Paragon Health Network, Sr. Sub. Notes, 9.500% due 11/1/07            918,000
    850,000   B-     Pharmaceutical Fine Chemicals, Sr. Sub. Notes,
                       9.750% due 11/15/07+ ....................................           962,625
                     Sun Healthhcare Group Inc., Sr. Sub. Notes:
  1,000,000   B2*      9.500% due 7/1/07 .......................................         1,015,000
  1,150,000   B2*      9.375% due 5/1/08 .......................................         1,161,500
                                                                                    --------------
                                                                                        10,641,875
                                                                                    --------------
</TABLE>

                       See Notes to Financial Statements.

                                       8
<PAGE>
 
<TABLE>
<CAPTION>

[LOGO]

                                                                  Schedule of Investments (continued)
                                                                            June 30, 1998 (unaudited)
=====================================================================================================
   Face
  Amount       Ratings                        Security                                     Value
-----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                            <C>
Hotel, Casinos and Gaming -- 2.9%
$ 1,500,000   B      Aztar Corp., Sr. Sub. Notes, 13.750% due 10/1/04 ..........    $    1,710,000
  2,000,000   B-     Courtyard By Marriott II, Sr. Secured Notes, 
                       10.750% due 2/1/08 ......................................         2,205,000
    620,000   BB+    Mohegan Tribal Gaming Authority, Sr. Secured Notes,
                       13.500% due 11/15/02 ....................................           800,575
                                                                                    --------------
                                                                                         4,715,575
                                                                                    --------------
Insurance -- 1.1%
  1,000,000   BB+    SIG Capital Trust, Guaranteed Notes, 9.500% due 8/15/27 ...         1,027,500
    650,000   BB-    Veritas Capital Trust, Guaranteed Notes, 10.000% due
                       1/1/28+ .................................................           682,500
                                                                                    --------------
                                                                                         1,710,000
                                                                                    --------------
Leisure -- 0.7%
  1,100,000   B3*    SFX Entertainment Inc., Sr. Sub. Notes, 9.125% due 2/1/08 .         1,083,500
                                                                                    --------------
Metals/Mining -- 2.1%
    400,000   B-     Haynes International Inc., Sr. Notes, 11.625% due 9/1/04 ..           444,000
  1,600,000   B2*    Kaiser Aluminum and Chemical Corp., Sr. Sub. Notes,
                       12.750% due 2/1/03 ......................................         1,700,000
    700,000   B2*    Koppers Industry Inc., Sr. Sub. Notes, 9.875% due 12/1/07 .           728,000
    500,000   B      WHX Corp., Sr. Notes, 10.500% due 4/15/05 .................           510,000
                                                                                    --------------
                                                                                         3,382,000
                                                                                    --------------
Oil and Natural Gas -- 5.0%
    500,000   B      Canadian Forest Oil Ltd., Sr. Sub. Notes, 8.750% due 
                       9/15/07 .................................................           492,500
  1,300,000   B+     Clark USA Inc., Sr. Notes, 10.875% due 12/1/05 ............         1,418,625
  1,350,000   Ba2*   Gulf Canada Resources Ltd., Sub. Debentures,
                       9.625% due 7/1/05 .......................................         1,451,250
                     Ocean Energy Inc., Sr. Sub. Notes:
    800,000   BB-      10.375% due 10/15/05 ....................................           886,000
    400,000   BB-      9.750% due 10/1/06 ......................................           438,000
    850,000   B+     Parker Drilling Co., Sr. Notes, 9.750% due 11/15/06 .......           871,250
  1,675,000   BB-    Santa Fe Energy Resources Inc., Sr. Sub. Debentures,
                       11.000% due 5/15/04 .....................................         1,817,375
    700,000   B2*    Stone Energy Corp., Sr. Sub. Notes, 8.750% due 9/15/07 ....           701,750
                                                                                    --------------
                                                                                         8,076,750
                                                                                    --------------
Oil Services -- 0.9%
    500,000   BB+    J. Ray McDermott SA, Sr. Sub. Notes, 9.375% due 7/15/06 ...           540,000
    900,000   BB     Pride Petroleum Services Inc., Sr. Notes, 9.375% due 5/1/07           950,625
                                                                                    --------------
                                                                                         1,490,625
                                                                                    --------------
</TABLE>

                       See Notes to Financial Statements.

                                       9
<PAGE>
 
<TABLE>
<CAPTION>

[LOGO]

                                                                  Schedule of Investments (continued)
                                                                            June 30, 1998 (unaudited)
=====================================================================================================
   Face
  Amount       Ratings                        Security                                     Value
-----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                            <C>
Packaging/Containers -- 1.2%
$   575,000   B      Huntsman Packaging Corp., Sr. Notes, 9.125% due 10/1/07+ ..    $      573,563
  1,000,000++ B      Impress Metal Packaging Holdings, Sr. Sub. Notes,
                       9.875% due 5/29/07 ......................................           581,717
    750,000   B-     Tekni-Plex Inc., Sr. Sub. Notes, 9.250% due 3/1/08+ .......           748,125
                                                                                    --------------
                                                                                         1,903,405
                                                                                    --------------
Paper/Forest Products and Printing -- 3.7%
  1,500,000   B      Goss Graphic Systems Inc., Sr. Sub. Notes,
                       12.000% due 10/15/06 ....................................         1,590,000
  4,025,000   B+     S.D. Warren Co., Sr. Sub. Notes, 12.000% due 12/15/04 .....         4,472,781
                                                                                    --------------
                                                                                         6,062,781
                                                                                    --------------
Pollution Control -- 1.1%
  1,000,000   B+     Allied Waste North America Inc., Sr. Sub. Notes,
                       10.250% due 12/1/06 .....................................         1,103,750
    675,000   BB-    Clisa SA, Guaranteed Sr. Notes, 11.625% due 6/1/04+ .......           673,312
                                                                                    --------------
                                                                                         1,777,062
                                                                                    --------------
Publishing -- 0.6%
    600,000++ B      Middleweb PLC, Sr. Notes, 10.500% due 5/30/08 .............         1,003,603
                                                                                    --------------
Real Estate -- 1.2%
    675,000   B-     BF Saul REIT, Sr. Notes, 9.750% due 4/1/08 ................           668,250
  1,115,000   Baa3*  Trizec Finance Ltd., Sr. Notes, 10.875% due 10/15/05 ......         1,261,344
                                                                                    --------------
                                                                                         1,929,594
                                                                                    --------------
Retail -- 0.9%
    650,000   B-     Advance Stores Co., Inc., Sr. Sub. Notes, 
                        10.250% due 4/15/08+ ...................................           675,188
    850,000   B-     US Office Products Co., Sr. Sub. Notes, 9.750% due 6/15/08+           852,125
                                                                                    --------------
                                                                                         1,527,313
                                                                                    --------------
Telecommunications -- 22.9%
  1,750,000   NR     Allegiance Telecommunicatons Inc., Units, step bond to 
                       yield 11.890% due 2/15/08 ...............................           929,688
  1,800,000   B3*    Clearnet Communications Inc., Sr. Discount Notes,
                       step bond to yield 13.653% due 12/15/05 .................         1,509,750
                     Colt Telecommunications Group PLC:
    250,000++ B        Sr. Notes, 10.125% due 11/30/07 .........................           450,495
  2,000,000   B        Step bond to yield 11.976% due 12/15/06 .................         1,580,000

</TABLE>

                       See Notes to Financial Statements.

                                       10
<PAGE>
 
<TABLE>
<CAPTION>

[LOGO]

                                                                  Schedule of Investments (continued)
                                                                            June 30, 1998 (unaudited)
=====================================================================================================
   Face
  Amount       Ratings                        Security                                     Value
-----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                            <C>
Telecommunications -- 22.9% (continued)
                     Dolphin Telecom PLC, Sr. Discount Notes:
$ 1,300,000   B-       Step bond to yield 11.362% due 6/1/08+ ..................    $      741,000
  1,125,000++ B-       Step bond to yield 11.625% due 6/1/08 ...................           694,825
                     Esprit Telecom Group PLC, Sr. Notes:
    700,000   B-       11.500% due 12/15/07 ....................................           722,750
    600,000++ B-       11.500% due 12/15/07 ....................................           342,382
    400,000   B-       10.875% due 6/15/08 .....................................           403,000
  1,025,000   NR     Facilicom International Inc., Sr. Notes, 10.500% due 
                       1/15/08 .................................................         1,022,438
  1,150,000   NR     Firstworld Communications, Units, step bond to yield
                       12.999% due 4/15/08 .....................................           517,500
  1,000,000   B      Hermes Eurorail Telecommunications Inc., Sr. Notes,
                       11.500% due 8/15/07 .....................................         1,131,250
    500,000   B+     Impsat Corp., Sr. Notes, 12.375% due 6/15/08 ..............           507,500
  2,275,000   B      Intermedia Communications, Sr. Discount Notes, step
                       bond to yield 12.351% due 5/15/06 .......................         1,871,188
  2,675,000   B-     Iridium LLC Capital Corp., Guaranteed Notes,
                       14.000% due 7/15/05 .....................................         2,982,625
  1,725,000   B+     McLeod Inc., Sr. Discount Notes, step bond to yield
                       10.594% due 3/1/07 ......................................         1,285,125
                     Metronet Communications Inc.:
  4,950,000   B        Sr. Discount Notes, step bond to yield 9.852% due 6/15/08         3,056,625
  1,650,000   B        Sr. Notes, 12.000% due 8/15/07+ .........................         1,914,000
  1,800,000   B2*    Nextel Communications Inc., Sr. Discount Notes,
                       step bond to yield 11.543% due 8/15/04 ..................         1,755,000
  1,150,000   B      Nextlink Communications, Sr. Notes, 12.500% due 4/15/06 ...         1,334,000
  2,075,000   NR     Pagemart Inc., Sr. Discount Notes, step bond to yield
                       11.250% due 2/1/08 ......................................         1,302,062
  1,325,000   B      Primus Telecommunications Group, Sr. Notes,
                       11.750% due 8/1/04 ......................................         1,407,813
    800,000   B-     Psinet Inc., Sr. Notes, 10.000% due 2/15/05 ...............           820,000
  2,750,000   BB+    Qwest Communications International Inc., Sr. Discount 
                     Notes, step bond to yield 9.351% due 10/15/07 .............         2,069,375
                     RCN Corp.:
  1,775,000   B3*      Sr. Discount Notes, step bond to yield
                        11.141% due 10/15/07 ...................................         1,136,000
  1,000,000   B3*      Sr. Notes, 10.000% due 10/15/07 .........................         1,030,000
    910,000   B-     RSL Communications Ltd., Sr. Notes, 12.250% due 11/15/06 ..         1,033,988
    500,000   NR     Startec Global Communications, Units, 12.000% due 5/15/08 .           491,250
</TABLE>

                       See Notes to Financial Statements.

                                       11
<PAGE>
 
<TABLE>
<CAPTION>

[LOGO]

                                                                  Schedule of Investments (continued)
                                                                            June 30, 1998 (unaudited)
=====================================================================================================
   Face
  Amount       Ratings                        Security                                     Value
-----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                            <C>
Telecommunications -- 22.9% (continued)
                     Telesystems International Wireless Corp., Sr. Discount Notes:
$ 1,300,000   CCC+     Step bond to yield 12.460% due 6/30/07 ..................    $      874,250
  1,100,000   CCC+     Step bond to yield 11.064% due 11/1/07 ..................           662,750
    700,000   CCC+   Thermadyne Holdings Corp., Debentures, step bond to
                       yield 12.500% due 6/1/08 ................................           388,500
    325,000   CCC+   Thermadyne Manufacturing LLC, Sr. Sub. Notes,
                       9.875% due 6/1/08 .......................................           327,844
    825,000   NR     Versatel Telecommunications, Units, 13.250% due 5/15/08 ...           870,375
                                                                                    --------------
                                                                                        37,165,348
                                                                                    --------------
Textiles -- 0.3%
    800,000++ B      Texon International, Sr. Notes, 10.000% due 2/1/08+ .......           443,213
                                                                                    --------------
Transportation -- 4.0%
    525,000   B      American Commercial Lines LLC, Bonds,
                       10.250% due 6/30/08+ ....................................           534,188
    600,000   B+     American Reefer Co. Ltd., 1st Mortgage, 10.250% due 3/1/08+           600,750
    500,000   BB     Enterprises Shipholding, Sr. Notes, 8.875 due 5/01/08+ ....           491,875
    200,000   BB     Guangzhou Shenzhen Superhighway, Sr. Notes,
                       10.250% due 8/15/07 .....................................           136,750
                     Sea Containers Ltd.:
    400,000   BB-      Sr. Notes, 7.875% due 2/15/08+ ..........................           395,000
  2,805,000   BB-      Sr. Sub. Debentures, 12.500% due 12/1/04 ................         3,166,144
    800,000   B+     Stena Line AB, Sr. Notes, 10.625% due 6/1/08 ..............           813,000
    425,000   B+     TBS Shipping International Ltd., First Mortgage,
                       10.000% due 5/1/05 ......................................           388,875
                                                                                    --------------
                                                                                         6,526,582
                                                                                    --------------

                     TOTAL CORPORATE BONDS AND NOTES
                     (Cost -- $145,279,723) ....................................       151,343,505
                                                                                    --------------
<CAPTION>

Shares                                        Security                                     Value
-----------------------------------------------------------------------------------------------------
<S>                  <C>                                                            <C>
PREFERRED STOCK -- 4.1%
Banking -- 0.3%
     20,100          California Federal Preferred Capital Corp.,
                       Series A, Exchange 9.125% ...............................           547,725
                                                                                    --------------
Broadcasting/Cable -- 3.8%
      5,531          Time Warner Inc., Series K, Exchange 10.250% ..............         6,153,238
                                                                                    --------------
                     TOTAL PREFERRED STOCK
                     (Cost -- $6,512,365) ......................................         6,700,963
                                                                                    --------------
</TABLE>

                       See Notes to Financial Statements.

                                       12
<PAGE>
 
<TABLE>
<CAPTION>

[LOGO]

                                                                  Schedule of Investments (continued)
                                                                            June 30, 1998 (unaudited)
=====================================================================================================

Shares                                        Security                                     Value
-----------------------------------------------------------------------------------------------------
<S>                  <C>                                                            <C>
WARRANTS -- 0.6%
Broadcasting -- 0.0%
      2,450          UIH Australia Inc., Expire 5/15/06# .......................    $       29,400
                                                                                    --------------
Telecommunications -- 0.6%
      1,750          Allegiance Telecommunications Inc., Expire 2/3/08# ........             4,375
      9,735          Clearnet Communications Inc., Expire 9/15/05+# ............            58,410
      2,000          Colt Telecommunications Warrants, Expire 12/31/06# ........           390,000
      1,000          Globalstar Telecommunications, Expire 2/15/04# ............           135,000
      1,000          Iridium World Communications Ltd., Expire 7/15/05# ........           140,000
     16,000          Metronet Communications, Expire 8/15/07# ..................            64,000
      7,130          Pagemart Inc., Expire 12/31/03+# ..........................            53,475
      1,325          Primus Telecommunications Group, Expire 8/1/04 # ..........            50,350
      1,300          RSL Communications Ltd., Expire 11/15/06# .................            52,000
                                                                                    --------------
                                                                                           947,610
                                                                                    --------------
                     TOTAL WARRANTS
                     (Cost -- $392,245) ........................................           977,010
                                                                                    --------------
<CAPTION>

  Face
  Amount                                      Security                                     Value
-----------------------------------------------------------------------------------------------------
<S>                  <C>                                                            <C>
REPURCHASE AGREEMENTS -- 2.0%
 $3,158,000          Goldman, Sachs & Co., 5.650% due 7/1/98;
                     Proceeds at maturity -- $3,158,495; (Fully collateralized
                     by U.S. Treasury Notes, 5.375% due 6/30/00;
                     Market value -- $3,222,662) (Cost -- $3,158,000) ..........         3,158,000
                                                                                    --------------
                     TOTAL INVESTMENTS -- 100%
                     (Cost -- $155,342,333** ) .................................    $  162,179,478
                                                                                    ==============
</TABLE>

----------

+    Security is exempt from registration under Rule 144A of Securities the 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 Statements.
 

                                       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 -- 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 that are 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>
 
<TABLE>
<CAPTION>
[LOGO]
                                                                         Statement of Assets and Liabilities
                                                                                   June 30, 1998 (unaudited)
============================================================================================================
<S>                                                                 <C>                        <C>
ASSETS:
   Investments, at value (Cost-- $155,342,333) ..................                              $ 162,179,478
   Cash .........................................................                                        375
   Interest and dividends receivable ............................                                  3,004,404
   Receivable for open forward foreign                                                       
      currency contracts (Note 11) ..............................                                     26,145
                                                                                               -------------
Total Assets ....................................................                                165,210,402
                                                                                               -------------
LIABILITIES:                                                                                 
   Bank loan (Note 7) ...........................................                                 30,000,000
   Investment advisory fees payable .............................                                    103,371
   Payable for securities purchased .............................                                    100,846
   Interest payable .............................................                                     91,442
   Administration fees payable ..................................                                     40,825
   Payable for open forward                                                                  
      foreign currency contracts (Note 11) ......................                                     11,136
   Accrued expenses .............................................                                    153,509
                                                                                               -------------
   Total Liabilities ............................................                                 30,501,129
                                                                                               -------------
Total Net Assets ................................................                              $ 134,709,273
                                                                                               =============
NET ASSETS:                                                                                  
   Par value of capital shares ..................................                              $     153,137
   Capital paid in excess of par value ..........................                                127,991,652
   7% Cumulative Preferred Stock (Note 6) .......................                                 30,000,000
   Overdistributed net investment income ........................                                   (595,849)
   Accumulated net realized loss                                                             
      from security transactions ................................                                (29,691,791)
   Net unrealized appreciation on                                                            
      investments and foreign currencies ........................                                  6,852,124
                                                                                               -------------
Total Net Assets ................................................                              $ 134,709,273
                                                                                               =============
                                                                       Per Share
                                                                    ---------------
NET ASSET VALUE, COMPRISED OF:
7% Cumulative Preferred Stock redemption value ..................   $      1,000.00            $  30,000,000
Cumulative undeclared dividends on 7.00%
   Preferred Stock ..............................................              3.16                   94,927
                                                                    ---------------            -------------
Total allocated to Preferred Stock ..............................   $      1,003.16               30,094,927
                                                                    ===============            -------------

Common Stock (15,313,686 shares outstanding) ....................   $          6.83              104,614,346
                                                                    ===============            -------------
Total Net Assets ................................................                              $ 134,709,273
                                                                                               =============
</TABLE>

                       See Notes to Financial Statements.


                                       15
<PAGE>
 
<TABLE>
<CAPTION>
[LOGO]

                                                         Statement of Operations
                                                      For the Three Months Ended
                                                       June 30, 1998 (unaudited)
================================================================================
<S>                                                                 <C>
INVESTMENT INCOME:
   Interest ....................................................    $ 3,883,410
   Dividends ...................................................        153,195
   Less: Interest expense (Note 7) .............................       (457,767)
                                                                    -----------
   Total Investment Income .....................................      3,578,838
                                                                    -----------
EXPENSES:
   Investment advisory fees (Note 2) ...........................        206,315
   Administration fees (Note 2) ................................         82,526
   Shareholder communications ..................................         43,630
   Audit and legal .............................................         24,079
   Directors' fees .............................................          8,726
   Shareholder and system servicing fees .......................          8,127
   Pricing .....................................................          7,735
   Custody .....................................................          1,795
   Other .......................................................         10,347
                                                                    -----------
   Total Expenses ..............................................        393,280
                                                                    -----------
Net Investment Income ..........................................      3,185,558
                                                                    -----------
REALIZED AND UNREALIZED GAIN (LOSS) ON INVESTMENTS
AND FOREIGN CURRENCIES (NOTES 3 AND 11):
   Realized Gain (Loss) From:
      Security transactions (excluding short-term securities) ..        669,550
      Foreign currency transactions ............................        (15,244)
                                                                    -----------
   Net Realized Gain ...........................................        654,306
                                                                    -----------
   Change in Net Unrealized Appreciation of
   Investments and Foreign Currencies:
      Beginning of period ......................................      9,425,614
      End of period ............................................      6,852,124
                                                                    -----------
   Decrease in Net Unrealized Appreciation .....................     (2,573,490)
                                                                    -----------
Net Loss on Investments and Foreign Currencies .................     (1,919,184)
                                                                    -----------
Increase in Net Assets From Operations .........................    $ 1,266,374
                                                                    ===========
</TABLE>


                       See Notes to Financial Statements.

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

                                                    June 30          March 31
                                                 -------------    -------------
<S>                                              <C>              <C>
OPERATIONS:
   Net investment income .....................   $   3,185,558    $  12,914,504
   Net realized gain .........................         654,306        1,717,025
   Increase (decrease) in net unrealized
      appreciation ...........................      (2,573,490)       6,555,506
                                                 -------------    -------------
   Increase in Net Assets From Operations ....       1,266,374       21,187,035
                                                 -------------    -------------
DIVIDENDS PAID FROM
NET INVESTMENT INCOME TO:
   7.00% Cumulative Preferred Stockholders ...      (1,050,000)      (2,100,000)
   Common Stockholders .......................      (2,788,814)     (11,728,952)
                                                 -------------    -------------
   Decrease In Net Assets From
      Distributions To Shareholders ..........      (3,838,814)     (13,828,952)
                                                 -------------    -------------
FUND SHARE TRANSACTIONS:
   Net value of shares issued for
      reinvestment of dividends ..............         799,314        3,448,238
                                                 -------------    -------------
   Increase in Net Assets From
      Fund Share Transactions ................         799,314        3,448,238
                                                 -------------    -------------
Increase (Decrease) in Net Assets ............      (1,773,126)      10,806,321
NET ASSETS:
   Beginning of period .......................     136,482,399      125,676,078
                                                 -------------    -------------
   End of period* ............................   $ 134,709,273    $ 136,482,399
                                                 =============    =============
* Includes undistributed (overdistributed)
   net investment income of: .................   $    (595,849)   $      72,651
                                                 =============    =============
</TABLE>

                       See Notes to Financial Statements.

   
                                       17
<PAGE>
 
<TABLE>
<CAPTION>
[LOGO]
                                                               Statement of Cash Flows
                                                            For the Three Months Ended
                                                              June 30,1998 (unaudited)
======================================================================================
<S>                                                       <C>             <C>
NET INCREASE IN CASH:
Cash Flows From Operating
and Investing Activities:
   Interest and dividends received ....................   $  4,006,233
   Operating expenses paid ............................       (389,199)
   Interest payments on bank loans ....................       (458,017)
   Purchases of short-term securities, net ............      3,151,000
   Purchases of long-term securities ..................    (38,161,303)
   Proceeds from disposition of long-term securities ..     34,891,047
                                                          ------------
   Net Cash Provided By Operating
     and Investing Activities .........................                   $  3,039,761
                                                                          ------------
Cash Flows From Financing Activities:
   Cash dividends paid on 7.00% Cumulative
     Preferred Stock ..................................     (1,050,000)
   Cash dividends paid on Common Stock* ...............     (1,989,500)
                                                          ------------
Net Cash Used By Financing Activities .................                     (3,039,500)
                                                                          ------------
Net Increase in Cash ..................................                            261
Cash--Beginning of Period .............................                            114
                                                                          ------------
Cash--End of Period ...................................                   $        375
                                                                          ============
RECONCILIATION OF INCREASE IN NET ASSETS
FROMOPERATIONS TO NET CASH PROVIDED
BY OPERATING AND INVESTING ACTIVITIES:
Increase in Net Assets From Operations ................                   $  1,266,374
   Amortization of discount on securities .............       (411,927)
   Decrease in investments ............................      2,454,941
   Decrease in receivable for securities sold .........        217,091
   Decrease in payable for securities purchased .......     (1,051,848)
   Decrease in dividends and interest receivable ......        537,714
   Increase in accrued expenses .......................         27,416
                                                          ------------
Total Adjustments .....................................                      1,773,387
                                                                          ------------
Net Cash Provided By Operating and Investing Activities                   $  3,039,761
                                                                          ============
</TABLE>

*    Exclusive of dividend reinvestment of $799,314.

                       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, payable semi-annually on June 15 and
December 15; (h) the net asset


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

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 (where the value of average daily net assets shall mean 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 (where 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 Smith Barney
Inc., another subsidiary of SSBH.

     3.   Investments

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

<TABLE>
================================================================================
<S>                                                                  <C>        
Purchases                                                            $37,109,455
--------------------------------------------------------------------------------
Sales                                                                 34,673,956
================================================================================
</TABLE>

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

<TABLE>
================================================================================
<S>                                                                 <C>       
Gross unrealized appreciation                                       $7,468,350
Gross unrealized depreciation                                         (631,205)
--------------------------------------------------------------------------------
Net unrealized appreciation                                         $6,837,145
================================================================================
</TABLE>

     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 agreements to resell the
securities to the sellers at a future date (generally, the next business


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

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 June 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 $94,927 at June 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 three months ended June 30, 1998 was $457,767.

     8.   Common Stock

     At June 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:

<TABLE>
<CAPTION>
                             Three Months Ended                 Year Ended
                               June 30, 1998                  March 31, 1998
                           ---------------------          ----------------------
                           Shares        Amount            Shares        Amount
================================================================================
<S>                        <C>          <C>               <C>         <C>
Shares issued on
   reinvestment            111,567      $799,314          460,479     $3,448,238
================================================================================
</TABLE>

                                       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:

<TABLE>
<CAPTION>
                              1999             2000             2003             2004
=========================================================================================
<S>                        <C>              <C>              <C>              <C>       
Carryforward Amounts       $14,407,000      $8,395,000       $4,873,000       $2,291,000
=========================================================================================
</TABLE>

     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 June 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 gain on the contracts is
reflected as follows:

<TABLE>
<CAPTION>
                                         Local          Market       Settlement     Unrealized
Foreign Currency                       Currency          Value          Date        Gain (Loss)
================================================================================================
<S>                                   <C>            <C>              <C>            <C>
To Sell:
British Pound                           280,906      $  467,244         8/24/98      $(11,136)
European Currency Unit                  676,312         745,141        11/30/98         9,881
German Mark                           2,563,158       1,425,575          9/2/98        16,264
-----------------------------------------------------------------------------------------------
Total Unrealized Gain on Open Forward
    Foreign Currency Contracts                                                        $15,009
===============================================================================================
</TABLE>


                                       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 period:

<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 ..........................          0.21              0.87            0.92
   Net realized and unrealized gain (loss) ........         (0.13)             0.56            0.08
                                                      -----------       -----------     -----------
   Total Income From Operations ...................          0.08              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 ......         (0.18)            (0.78)          (0.72)
   Change in accumulated undeclared dividends
      on Preferred Stock ..........................          0.04                --              --
                                                      -----------       -----------     -----------
   Total Distributions ............................         (0.21)            (0.92)          (0.86)
                                                      -----------       -----------     -----------
Net Asset Value, End of Period ....................         $6.83             $6.96           $6.45
                                                      ===========       ===========     ===========
Market Value, End of Period .......................         $7.63             $7.50           $7.25
                                                      ===========       ===========     ===========
Total Return, Based on Market Value* ..............          4.35%++          14.81%          15.55%
                                                      ===========       ===========     ===========
Total Return, Based on Net Asset Value* ...........          0.66%++          19.75%          14.04%
                                                      ===========       ===========     ===========
Net Assets**, End of Period (000's) ...............      $104,614          $105,861         $95,034
                                                      ===========       ===========     ===========
Ratios to Average Net Assets Based on
Common Shares Outstanding***:
   Net Investment Income ..........................         12.12%+           12.60%          14.35%
   Interest Expense ...............................          1.74+             1.81            1.92
   Other Expenses .................................          1.50+             1.51            1.59

Portfolio Turnover Rate ...........................            22%               79%            101%
</TABLE>

----------
(1)  For the three months ended June 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 stock outstanding throughout each year:

<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                    2,740       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)                     164,600     165,900      154,800     149,400           --          --
</TABLE>

----------
(1)  For the three months ended June 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
</TABLE>

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


                                       27
<PAGE>
 
[LOGO]

                                                      Financial Data (unaudited)
================================================================================

For a share of common stock outstanding throughout each period:

<TABLE>
<CAPTION>
                                                                                   Dividend
        Record         Payable         NYSE         Net Asset      Dividend      Reinvestment
         Date           Date       Closing Price     Value*          Paid            Price
=============================================================================================
<S>                   <C>             <C>            <C>            <C>             <C>   
        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
=============================================================================================
</TABLE>

* 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 the 


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

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
with respect to any subsequent dividends or distributions, on the first trading
day


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

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 of any securities mentioned in the report.

                                  FD01153 8/98
================================================================================