<PAGE>
 
================================================================================

     ZENIX
    Income
   Fund Inc.






                                   [GRAPHIC]






                                        Annual Report
                                        March 31, 1998


================================================================================
<PAGE>
 
-----------------------------------[GRAPHIC]------------------------------------

                             Zenix Income Fund Inc.



Dear Shareholder:

     We are pleased to provide the annual report for the Zenix Income Fund Inc.
("Fund") for the year ended March 31, 1998. During the past year, the Fund
distributed income dividends totaling $0.78 per share. The table below shows the
annualized distribution rate and twelve-month total return for the Fund based on
its March 31, 1998 net asset value ("NAV") per share and its New York Stock
Exchange ("NYSE") closing price.

<TABLE>
<CAPTION>
              Price                  Annualized               One-Year
            Per Share             Distribution Rate         Total Return
            ---------             -----------------         ------------
           <S>                         <C>                    <C>   
           $6.96 (NAV)                 10.52%                 19.75%
           $7.50 (NYSE)                 9.76%                 14.81%
</TABLE>

     The Zenix Income Fund generated a total return on NAV of 19.75% for the
year ended March 31, 1998 and outperformed the twelve-month average total return
for closed-end high yield bond funds of 17.76% for the same time period as
reported by Lipper Analytical Services, Inc. (Lipper is an independent
fund-tracking organization.)

Market and Economic Overview

     The high yield bond market generated positive performance during the six
months ended March 31, 1998 with total returns in the 5%-to-6% range. In the
first quarter of 1998, the high yield bond market continued to generate
competitive performance returns. The lower quality issues generally outperformed
the higher quality issues as the performance of the lower quality issues tends
to correlate more closely to the U.S. stock market.

     During the first quarter of 1998 the U.S. stock market rose by 10% to 15%
depending upon which stock market index was used. A strong U.S. economy,



                                       1

-----------------------------------[GRAPHIC]------------------------------------
<PAGE>
 
ample liquidity in the financial markets and moderate inflation continued to
fuel the stock markets. Interest rates remained confined to a narrow range with
little change in the rates of intermediate- and long-term U.S. Treasury
securities. The Federal Reserve Board ("Fed") continued to remain on the
sidelines, and federal-funds rates remained unchanged at 5.50%.

     While the Asian crisis did not dampen U.S. economic growth, it did keep
pressure on worldwide inflation with price declines on a number of important
global commodities such as oil. The net result was extremely positive for U.S.
financial markets, particularly the U.S. stock market. The U.S. bond market was
stuck in a narrow trading range and we believe the bond market will probably
continue to trade in a narrow range so long as the Fed's monetary policy remains
on hold. However, in recent weeks, the Fed has grown more concerned over strong
U.S. economic growth and the possibility that inflation may be increasing. Yet
the evidence so far suggests otherwise, with most statistics indicating
relatively tame inflation during the first quarter of 1998.

     During the first three months of 1998, the stock markets experienced high
volatility with most major indices again moving toward record highs. Despite
record new issuance, the high yield bond market also generated strong
performance results in the first quarter. In our view, this was likely in
reaction to continued strength in the U.S. stock markets.


Portfolio Strategy and Market Outlook

     During the past three months, we became more conservative and increased our
weighting in higher-quality, defensive issues. We continue to believe that the
U.S. economy's outlook remains mixed and that many consumer-sensitive industries
will continue to experience fierce price competition. In addition, the
significant problems in Asia could also put severe pressure on commodity goods
prices as troubled Asian companies attempt to increase their exports to the rest
of the world to make up for the expected economic declines in their own region.
Moreover, we believe that a slowdown in overall world economic growth may occur
in the coming months as the severe economic decline in Asia sharply reduces
demand for many U.S. and European products. Consequently, the first half of 1998
could experience a slight increase in the default rates of select high yield
credits, especially weaker, more vulnerable companies that are having difficulty
competing. Given the increased uncertainty over Asia, we would expect stock
market volatility to further rise in the coming months.


                                       2

-----------------------------------[GRAPHIC]------------------------------------
<PAGE>
 
     We will, therefore, still avoid these areas of the U.S. economy where
consumer spending is weak as well as industries facing heavy pricing
competition. Our emphasis will be on industries that are experiencing strong
growth such as telecommunications, media, and cable television. We also plan on
owning stronger rated B and BB bonds and avoid the weaker, lower tier issues
that are generally in the CCC/Caa rating category. We believe our conservative
investment strategy is a prudent course of action given the higher risks and
volatility we expect in the world's financial markets going forward.

     In closing, thank you for investing in the Zenix Income Fund. We look
forward to continuing to help you pursue your investment goals. If you have any
questions about 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

May 4, 1998


--------------------------------------------------------------------------------
Special Shareholder Notice

     The Fund's Board of Directors authorized a change in the Fund's investment
policy pertaining to investments in restricted or illiquid securities. Because
the policy is currently "fundamental," the change requires shareholder approval,
and the Fund intends to include a proposal to this effect in the proxy statement
for the Annual Meeting of Shareholders, which should be distributed to
shareholders shortly. If approved by shareholders, the new policy would permit
the Fund to invest without limitation in restricted securities determined to be
liquid. Such securities would primarily consist of those offered to and resold
among Qualified Institutional Buyers pursuant to Rule 144a under the Securities
Act. The Fund's investment objective, and other investment policies, would
remain unchanged.
--------------------------------------------------------------------------------

                                       3

-----------------------------------[GRAPHIC]------------------------------------
<PAGE>
 
--------------------------------------------------------------------------------


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

Take Advantage of the Fund's Dividend Reinvestment Policy!

     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, 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 Dividend Reinvestment 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 Dividend Reinvestment Plan
and about how you can participate, please call First Data Investors Services
Group, Inc. at (800) 331-1710.

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

                                       4

-----------------------------------[GRAPHIC]------------------------------------
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                                                             Schedule of Investments
                                                                                      March 31, 1998
====================================================================================================

   Face
  Amount    Ratings                           Security                                     Value
----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                               <C>    
CORPORATE BONDS AND NOTES -- 91.7%
Aerospace/Defense -- 2.1%
$ 2,500,000   BB     Airplanes Pass Through Trust, Corporate Collateralized
                       Mortgage Obligation, 10.875% due 3/15/19 .....................  $ 2,815,175
    650,000   BB     Morgan Stanley Aircraft Finance, Corporate Collateralized
                       Mortgage Obligation, 8.700% due 3/15/23 ......................      661,375
                                                                                       -----------
                                                                                         3,476,550
                                                                                       -----------
Banking -- 1.1%
  1,525,000   B      First Nationwide Parent Holdings Ltd.,
                       Sr. Notes, 12.500% due 4/15/03 ...............................    1,749,937
                                                                                       -----------
Broadcasting/Cable -- 12.2%
  1,500,000   B2*    Comcast UK Cable, Debentures, step bond to yield
                       11.175% due 11/15/07 .........................................    1,248,750
                     CSC Holdings Inc., Sr. Sub. Debentures:
  2,975,000   BB-      9.875% due 2/15/13 ...........................................    3,294,812
  1,000,000   BB-      10.500% due 5/15/16 ..........................................    1,175,000
    550,000   BB-      9.875% due 4/1/23 ............................................      611,875
                     Marcus Cable Co. LP:
  2,000,000   B3*      Sr. Debentures, 11.875% due 10/1/05 ..........................    2,172,500
    500,000   B        Sr. Notes, step bond to yield 12.747% due 12/15/05 ...........      455,000
  1,500,000   B-     PX Escrow Corp., Sr. Discount Notes, step bond to yield
                       9.287% due 2/1/06 ............................................    1,070,625
                     Rogers Cablesystems of America, Inc.:
    850,000   BB+      Sr. Notes, Series B, 10.000% due 3/15/05 .....................      947,750
                       Sr. Sub. Debentures:
  1,000,000   BB+       10.000% due 12/1/07 .........................................    1,117,500
  2,100,000   BB-       11.000% due 12/1/15 .........................................    2,480,625
    900,000   BB-    Rogers Communications Inc., Sr. Notes, 8.875% due 7/15/07 ......      915,750
                     TV Azteca SA, Guaranteed Sr. Notes:
    525,000   Ba3*     Series A, 10.125% due 2/15/04 ................................      551,250
    950,000   Ba3*     Series B, 10.500% due 2/15/07 ................................    1,016,500
  3,050,000   B      United International Holdings Inc., Sr. Discount Notes,
                       step bond to yield 10.723% due 2/15/08+ ......................    1,910,063
  1,000,000   BBB-   Videotron Group Ltd., Sr. Notes, 10.625% due 2/15/05 ...........    1,122,500
                                                                                       -----------
                                                                                        20,090,500
                                                                                       -----------
</TABLE>


                       See Notes to Financial Statements.

                                       5
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                                                  Schedule of Investments(continued)
                                                                                      March 31, 1998
====================================================================================================

   Face
  Amount    Ratings                           Security                                     Value
----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                               <C>    
Building/Construction -- 0.8%
$ 1,115,000   B-     Trizec Finance Ltd., Sr. Notes, 10.875 due 10/15/05 ............  $ 1,264,131
                                                                                       -----------
Chemicals -- 2.2%
    950,000   CCC+   Interlake Corp., Sr. Sub. Debentures, 12.125% due 3/1/02 .......      985,625
  1,000,000   B1*    NL Industries Inc., Sr. Secured Notes, 11.750% due 10/15/03 ....    1,110,000
  1,500,000   B      Unifrax Investment Corp., Sr. Notes, 10.500% due 11/1/03 .......    1,567,500
                                                                                       -----------
                                                                                         3,663,125
                                                                                       -----------
Consumer Durables -- 0.3%
    450,000   B-     Eagle-Picher Industrial Inc., Sr. Sub. Notes,
                       9.375% due 3/1/08 ............................................      459,000
                                                                                       -----------
Diversified Manufacturing -- 1.3%
  1,325,000   B      Imperial Holly Corp., Sr. Sub. Notes, 9.750% due 12/15/07 ......    1,368,063
    700,000   B+     Park-Ohio Industries, Sr. Sub. Notes, 9.250% due 12/1/07 .......      738,500
                                                                                       -----------
                                                                                         2,106,563
                                                                                       -----------
Electric Utilities -- 4.8%
                     AES Corp., Sr. Sub. Notes:
    425,000   B+       8.375% due 8/15/07 ...........................................      436,687
  2,225,000   B+       8.500% due 11/1/07 ...........................................    2,302,875
                     Calpine Corp., Sr. Notes:
  1,350,000   Ba2*     10.500% due 5/15/06 ..........................................    1,491,750
    750,000   Ba2*     8.750% due 7/15/07 ...........................................      774,375
    650,000   BB+    Cleveland Electric Illuminating, Sr. Notes,
                       7.430% due 11/1/09+ ..........................................      673,562
    650,000   BB+    El Paso Electric Co., First Mortgage, 8.900% due 2/1/06 ........      723,125
    891,853   BB     Midland Cogeneration Venture Limited Partnership,
                       Midland Funding, Sr. Secured Lease Obligation Bond,
                       Series C, 10.330% due 7/23/02 ................................      959,857
    425,000   BBB-   Niagara Mohawk Power, First Mortgage,
                       7.750% due 5/15/06 ...........................................      448,906
                                                                                       -----------
                                                                                         7,811,137
                                                                                       -----------
Electronics-Computers -- 6.0%
  1,000,000   B      Celestica International Inc., Sr. Sub. Notes,
                       10.500% due 12/31/06 .........................................    1,092,500
  1,500,000   B      Fairchild Semiconductor Inc., Sr. Sub. Notes,
                       10.125% due 3/15/07 ..........................................    1,567,500
  1,000,000   B-     Graphic Controls Corp., Sr. Sub. Notes,
                       12.000% due 9/15/05 ..........................................    1,122,500
</TABLE>


                       See Notes to Financial Statements.

                                       6
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                                                  Schedule of Investments(continued)
                                                                                      March 31, 1998
====================================================================================================

   Face
  Amount    Ratings                           Security                                     Value
----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                             <C>    
Electronics-Computers -- 6.0% (continued)
                     Unisys Corp., Sr. Notes:
 $1,800,000   B+       12.000% due 4/15/03 .......................................... $  2,052,000
  2,325,000   B+       11.750% due 10/15/04 .........................................    2,699,906
  1,200,000   B-     Viasystems Inc., Sr. Sub. Notes, 9.750% due 6/1/07 .............    1,260,000
                                                                                      ------------
                                                                                         9,794,406
                                                                                      ------------
Electronics-Technology -- 0.4%
    650,000   B-     Axiohm Transaction Solutions, Sr. Sub. Notes,
                       9.750% due 10/1/07 ...........................................      663,000
                                                                                      ------------
Engineering/Construction -- 0.4%
    675,000   BB-    Clisa SA, Guaranteed Sr. Notes, 11.625% due 6/1/04+ ............      698,625
                                                                                      ------------

Finance -- 4.2%
  1,500,000   B      Amresco Inc., Sr. Sub. Notes, Series A, 10.000% due 3/15/04 ....    1,563,750
  1,000,000   B2*    Intertek Finance PLC., Sr. Sub. Notes, Series B,
                       10.250% due 11/1/06 ..........................................    1,063,750
  1,000,000   B2*    Ocwen Capital Trust, Guaranteed Notes,
                       10.875% due 8/1/27 ...........................................    1,110,000
  2,750,000   BB-    Ocwen Financial Corp., Notes, 11.875% due 10/1/03 ..............    3,141,875
                                                                                      ------------
                                                                                         6,879,375
                                                                                      ------------
Foods -- 2.2%
    425,000   B+     Ameriserve Food Distributors Inc., Guaranteed Notes,
                       8.875% due 10/15/06 ..........................................      438,812
    850,000   B-     B&G Foods Inc., Sr. Sub. Notes, 9.625% due 8/1/07 ..............      873,375
    650,000   B      Purina Mills Inc., Sr. Sub. Notes, 9.000% due 3/15/10+ .........      672,750
  1,500,000   B2*    Van De Kamp Inc., Sr. Sub. Notes, 12.000% due 9/15/05 ..........    1,680,000
                                                                                      ------------
                                                                                         3,664,937
                                                                                      ------------
Healthcare/Drugs/Hospital Supplies -- 5.0%
    950,000   B-     Fisher Scientific International Inc., Sr. Sub. Notes,
                       9.000% due 2/1/08 ............................................      971,375
  1,025,000   B+     Fresenius Medical Capital Trust II, Guaranteed Notes,
                       7.875% due 2/1/08 ............................................    1,025,000
  1,600,000   BB     ICN Pharmaceutical Inc., Sr. Notes, 9.250% due 8/15/05 .........    1,700,000
  1,000,000   B2*    Integrated Health Services Inc., Sr. Sub. Notes,
                       9.250% due 1/15/08 ...........................................    1,053,750
  1,700,000   B-     Magellan Health Services Inc., Sr. Sub. Notes,
                       9.000% due 2/15/08+ ..........................................    1,721,250
</TABLE>


                       See Notes to Financial Statements.

                                       7
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                                                  Schedule of Investments(continued)
                                                                                      March 31, 1998
====================================================================================================

   Face
  Amount    Ratings                           Security                                     Value
----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                               <C>    
Healthcare/Drugs/Hospital Supplies -- 5.0% (continued)
$   900,000   B-     Paragon Health Network, Sr. Sub. Notes,
                       9.500% due 11/1/07 ...........................................  $   929,250
    850,000   B-     Pharmaceutical Fine Chemicals, Sr. Sub. Notes,
                       9.750% due 11/15/07+ .........................................      878,688
                                                                                       -----------
                                                                                         8,279,313
                                                                                       -----------
Hotel, Casinos and Gaming -- 6.7%
  1,500,000   B2*    Aztar Corp., Sr. Sub. Notes, 13.750% due 10/1/04 ...............    1,730,625
  2,000,000   B-     Courtyard By Marriott II, Sr. Secured Notes,
                       10.750% due 2/1/08 ...........................................    2,215,000
    600,000   B2*    Extended Stay America, Sr. Sub. Notes, 9.150% due 3/15/08 ......      606,000
    300,000   Ba3*   HMC Acquisition Properties Inc., Sr. Notes,
                       Series B, 9.000% due 12/15/07 ................................      315,750
                     HMH Properties Inc., Sr. Notes:
  3,330,000   BB-      Series B, 9.500% due 5/15/05 .................................    3,546,450
    800,000   BB-      Series B, 8.875% due 7/15/05 .................................      846,000
    620,000   Ba1*   Mohegan Tribal Gaming Authority, Sr. Secured Notes,
                       13.500% due 11/15/02 .........................................      801,350
    950,000   B      Signature Resorts Inc., Sr. Sub. Notes,
                       9.750% due 10/1/07 ...........................................      969,000
                                                                                       -----------
                                                                                        11,030,175
                                                                                       -----------
Insurance -- 0.7%
    500,000   BB+    SIG Capital Trust, Guaranteed Notes, 9.500% due 8/15/27 ........      515,625
    650,000   BB-    Veritas Capital Trust, Guaranteed Notes, 10.000% due 1/1/28+ ...      684,125
                                                                                       -----------
                                                                                         1,199,750
                                                                                       -----------
Leisure -- 0.6%
    400,000   B-     Premier Parks Inc., Sr. Discount Notes,
                       step bond to yield 10.000% due 4/1/08 ........................      255,500
    800,000   B3*    SFX Entertainment Inc., Sr. Sub Notes, 9.125% due 2/1/08+ ......      792,000
                                                                                       -----------
                                                                                         1,047,500
                                                                                       -----------
Machinery -- 0.3%
    500,000   B-     Alvey Systems Inc., Sr, Sub. Notes, 11.375% due 1/31/03 ........      523,125
                                                                                       -----------
Metals/Mining -- 3.5%
  2,400,000   B-     Haynes International Inc., Sr. Notes, 11.625% due 9/1/04 .......    2,721,000
  1,600,000   B2*    Kaiser Aluminum and Chemical Corp., Sr. Sub. Notes,
                       12.750% due 2/1/03                                                1,704,000
</TABLE>


                       See Notes to Financial Statements.

                                       8
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                                                  Schedule of Investments(continued)
                                                                                      March 31, 1998
====================================================================================================

   Face
  Amount    Ratings                           Security                                     Value
----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                               <C>    
Metals/Mining -- 3.5% (continued)
$   700,000   B2*    Koppers Industry Inc., Sr. Sub. Notes, 9.875% due 12/1/07 ......  $   742,000
    500,000   BB-    J. Ray McDermott SA, Sr. Sub. Notes,
                       9.375% due 7/15/06 ...........................................      541,250
                                                                                       -----------
                                                                                         5,708,250
                                                                                       -----------
Oil/Natural Gas -- 7.5%
    500,000   B      Canadian Forest Oil Ltd., Sr. Sub. Notes,
                       8.750% due 9/15/07 ...........................................      511,250
  1,300,000   B+     Clark USA Inc., Sr. Notes, 10.875% due 12/1/05 .................    1,434,875
  1,425,000   B+     Dawson Production Services Inc., Sr. Notes,
                       9.375% due 2/1/07 ............................................    1,469,531
  1,350,000   Ba2*   Gulf Canada Resources Ltd., Sub. Debentures,
                       9.625% due 7/1/05 ............................................    1,468,125
                     Ocean Energy Inc.:
    800,000   B        Sr. Sub. Notes, 10.375% due 10/15/05 .........................      888,000
    400,000   B-       Sr. Unsecured Notes, 9.750% due 10/1/06 ......................      441,000
                     Parker Drilling Co.:
  1,800,000   B+       Sr. Notes, 9.750% due 11/15/06 ...............................    1,930,500
    700,000   B+       Sr. Unsecured Notes, 9.750% due 11/15/06+ ....................      750,750
    900,000   BB     Pride Petroleum Services Inc., Sr. Notes,
                       9.375% due 5/1/07 ............................................      960,750
  1,675,000   BB-    Santa Fe Energy Resources Inc., Sr. Sub. Debentures,
                       11.000% due 5/15/04 ..........................................    1,821,563
    700,000   B2*    Stone Energy Corp., Sr. Sub. Notes, 8.750% due 9/15/07 .........      718,375
                                                                                       -----------
                                                                                        12,394,719
                                                                                       -----------
Packaging/Containers -- 1.3%
    750,000   B      Huntsman Packaging Corp., Sr. Notes,
                       9.125% due 10/1/07+ ..........................................      765,938
  1,000,000++ B      Impress Metal Packaging Holdings, Sr. Sub. Notes,
                       9.875% due 5/29/07 ...........................................      579,242
    750,000   B-     Tekni-Plex Inc., Sr. Sub Notes, 9.250% due 3/1/08+ .............      772,500
                                                                                       -----------
                                                                                         2,117,680
                                                                                       -----------
Paper/Forest Products and Printing -- 4.1%
  1,300,000   B-     American Pad & Paper Co., Sr. Sub. Notes, Series B,
                       13.000% due 11/15/05 .........................................    1,316,250
  1,500,000   B      Goss Graphic Systems Inc., Sr. Sub. Notes,
                       12.000% due 10/15/06 .........................................    1,706,250
  3,275,000   B+     S.D. Warren Co., Sr. Sub. Notes, 12.000% due 12/15/04 ..........    3,663,906
                                                                                       -----------
                                                                                         6,686,406
                                                                                       -----------
</TABLE>


                       See Notes to Financial Statements.

                                       9
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                                                  Schedule of Investments(continued)
                                                                                      March 31, 1998
====================================================================================================

   Face
  Amount    Ratings                           Security                                     Value
----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                               <C>    
Pollution Control -- 0.7%
$ 1,000,000   B+     Allied Waste North America Inc., Sr. Sub. Notes,
                       10.250% due 12/1/06 ..........................................  $ 1,115,000
                                                                                       -----------
Real Estate -- 0.3%
    425,000   B-     BF Saul REIT, Sr. Notes, 9.750% due 4/1/08 .....................      430,313
                                                                                       -----------
Telecommunications -- 19.7%
    750,000   NR     Allegiance Telecom Inc., Units, step bond to yield
                       11.713% due 2/15/08 ..........................................      435,000
    400,000   NR     American Mobile Satellite, Units, 12.250% due 4/1/08 ...........      416,000
    450,000++ B2*    Cellular Communications International Inc.,
                       Sr. Discount Notes, step bond to yield 9.55% due 4/1/05+ .....      321,785
  1,225,000   BB-    Century Communications Corp., Sr. Notes,
                       8.750% due 10/1/07 ...........................................    1,277,062
  2,100,000   B3*    Clearnet Communications Inc., Sr. Discount Notes,
                       step bond to yield 13.778% due 12/15/05 ......................    1,743,000
                     Colt Telecommunications Group PLC:
    250,000++ B        Sr. Notes, 10.125% due 11/30/07 ..............................      452,140
  2,000,000   B        Step bond to yield 11.976% due 12/15/06 ......................    1,760,000
                     Esprit Telecom Group PLC, Sr. Notes:
    700,000   B-       11.500% due 12/15/07 .........................................      772,625
  1,375,000++ B-       11.500% due 12/15/07 .........................................      817,833
    425,000   NR     Facilicom International Inc., Sr. Notes, 10.500% due 1/15/08 ...      445,187
  1,100,000   B2*    Fonorola Inc., Sr. Notes, 12.500% due 8/15/02 ..................    1,230,625
    700,000   B      Hermes Eurorail Telecommunications Inc., Sr. Notes,
                       11.500% due 8/15/07 ..........................................      794,500
  2,275,000   B      Intermedia Communications, Sr. Discount Notes,
                       step bond to yield 12.351% due 5/15/06 .......................    1,879,719
  1,675,000   B-     Iridium LLC Capital Corp., Guaranteed Notes,
                       14.000% due 7/15/05 ..........................................    1,949,281
  1,725,000   B+     McLeod Inc., Sr. Discount Notes, step bond to yield
                       10.594% due 3/1/07 ...........................................    1,321,781
  1,600,000   NR     Metronet Communications Inc., Sr. Notes,
                       12.000% due 8/15/07 ..........................................    1,852,000
  2,100,000   B2*    Nextel Communications Inc., Sr. Discount Notes,
                       step bond to yield 11.565% due 8/15/04 .......................    2,021,250
  1,150,000   B      Nextlink Communications, Sr. Notes,
                       12.500% due 4/15/06 ..........................................    1,332,563
  1,050,000   B      Netia Holdings BV, Guaranteed Notes, 10.250% due 11/1/07+ ......    1,081,500
    200,000   NR     Orbital Imaging Corp., 11.625% due 3/1/05 ......................      220,000
  2,075,000   Caa2*  Pagemart Inc., Sr. Discount Notes,
                       step bond to yield 11.250% due 2/1/08                             1,276,125
</TABLE>


                       See Notes to Financial Statements.

                                       10
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                                                  Schedule of Investments(continued)
                                                                                      March 31, 1998
====================================================================================================

   Face
  Amount    Ratings                           Security                                     Value
----------------------------------------------------------------------------------------------------
<S>           <C>    <C>                                                               <C>    
Telecommunications -- 19.7% (continued)
$ 1,325,000   B-     Primus Telecommunications Group, Sr. Notes,
                       11.750% due 8/1/04 ...........................................  $ 1,484,000
  2,750,000   B+     Qwest Communications International Inc., Sr. Discount Notes,
                       step bond to yield 9.351% due 10/15/07 .......................    2,024,688
                     RCN Corp.:
  1,775,000   B3*      Sr. Discount Notes, step bond to yield
                        11.141% due 10/15/07 ........................................    1,202,563
  1,000,000   B3*      Sr. Notes, 10.000% due 10/15/07 ..............................    1,070,000
  1,300,000   B-     RSL Communications Ltd., Sr. Notes,
                       12.250% due 11/15/06 .........................................    1,480,375
    400,000   B-     Satelites Mexicanos SA, Sr. Notes, 10.125% due 11/1/04 .........      412,000
                     Telesystems International Wireless Corp., Sr. Discount Notes:
    700,000   B-       Step bond to yield 13.250% due 6/30/07 .......................      490,000
    650,000   B-       Step bond to yield 10.514% due 11/1/07 .......................      416,000
    600,000   NR     Wam!Net Inc., step bond to yield 13.250% due 3/1/05 ............      366,000
                                                                                       -----------
                                                                                        32,345,602
                                                                                       -----------
Textiles -- 0.3%
    800,000++ B      Texon International, Sr. Notes, 10.000% due 2/1/08+ ............      448,794
                                                                                       -----------
Transportation -- 3.0%
    600,000   B+     American Reefer Co. Ltd., First Mortgage,
                       10.250% due 3/1/08 ...........................................      603,000
    950,000   BB     Guangzhou Shenzhen Superhighway, Sr. Notes,
                       10.250% due 8/15/07 ..........................................      808,688
                     Sea Containers Ltd.:
    400,000   BB-      Sr. Notes, 7.875% due 2/15/08+ ...............................      396,000
  2,805,000   BB-      Sr. Sub. Debentures, 12.500% due 12/1/04 .....................    3,169,650
                                                                                       -----------
                                                                                         4,977,338
                                                                                       -----------
                     TOTAL CORPORATE BONDS AND NOTES
                     (Cost-- $141,755,747) ..........................................  150,625,251
                                                                                       -----------
</TABLE>

<TABLE>
<CAPTION>
  Shares                                      Security                                     Value
--------------------------------------------------------------------------------------------------
<S> <C>             <C>                                                                   <C>
 PREFERRED STOCK -- 4.1%
Banking -- 0.3%
    20,100          California Federal Preferred Capital Corp.,
                       Series A, Exchange 9.125% ....................................      552,750
                                                                                       -----------
</TABLE>


                       See Notes to Financial Statements.

                                       11
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                                                  Schedule of Investments(continued)
                                                                                      March 31, 1998
====================================================================================================

  Shares                                      Security                                     Value
--------------------------------------------------------------------------------------------------
<S>   <C>            <C>                                                               <C>
Broadcasting/Cable -- 3.8%
      5,531          Time Warner Inc., Series K, Exchange 10.250% ...................  $ 6,187,806
                                                                                       -----------
                     TOTAL PREFERRED STOCK
                     (Cost-- $6,512,365) ............................................    6,740,556
                                                                                       -----------
WARRANTS -- 0.3%
Broadcasting/Cable -- 0.0%
      2,450          UIH Australia Inc., Expire 5/15/06# ............................       29,400
                                                                                       -----------
Telecommunications -- 0.3%
      9,735          Clearnet Communications Inc., Expire 9/15/05+# .................       58,410
      1,000          Globalstar Telecommunications, Expire 2/15/04# .................      140,000
      1,000          Iridium World Communications Ltd., Expire 7/15/05# .............      140,000
      1,600          Metronet Communications, Expire 8/15/07# .......................       32,000
      7,130          Pagemart Inc., Expire 12/31/20+# ...............................       53,475
      1,325          Primus Telecommunications Group expires 8/1/04# ................       42,400
      1,300          RSL Communications Ltd., Expire 11/15/06# ......................       52,000
                                                                                       -----------
                                                                                           518,285
                                                                                       -----------
                     TOTAL WARRANTS
                     (Cost-- $257,505)                                                     547,685
                                                                                       -----------
</TABLE>

<TABLE>
<CAPTION>
   Face
  Amount                                      Security                                     Value
--------------------------------------------------------------------------------------------------
<S>                   <C>                                                             <C>         
REPURCHASE AGREEMENT-- 3.9%
 $6,309,000          Goldman, Sachs & Co., 5.850% due 4/1/98;
                     Proceeds at maturity-- $6,310,024; (Fully collateralized
                     by U.S. Treasury Notes, 5.375% due 1/31/00;
                     Market value-- $6,437,968) (Cost-- $6,309,000)                      6,309,000
                                                                                      ------------

                     TOTAL INVESTMENTS -- 100%
                     (Cost-- $154,834,617**)                                          $164,222,492
                                                                                      ============
</TABLE>

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

     See page 13 for definition of ratings.

                       See Notes to Financial Statements.

                                       12
<PAGE>
 
[GRAPHIC]
                                                                    Bond Ratings
================================================================================
All ratings are by Standard & Poor's Ratings Service ("Standard & Poor's"),
except those identified by an asterisk (*) are rated by Moody's Investors
Service, Inc. ("Moody's"). The definitions of the applicable rating symbols are
set forth below:

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

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

BB       -- Bonds rated "BB" have less near-term vulnerability to default than
            other speculative issues. However, it faces major ongoing
            uncertainties or exposure to adverse business, financial, or
            economic conditions which could lead to inadequate capacity to meet
            timely interest and principal payments.

B        -- Bonds rated "B" have a greater vulnerability to default but
            currently have the capacity to meet interest and principal payments.
            Adverse business, financial, or economic conditions will likely
            impair capacity or willingness to pay interest and repay principal.
            The "B" rating category is also used for debt, subordinated to
            senior debt, that is assigned an actual or implied "BB" or "BB-"
            rating.

CCC      -- Bonds rated "CCC" have a currently identifiable vulnerability to
            default, and are dependent upon favorable business, financial, and
            economic conditions to meet timely payment of interest and repayment
            of principal. In the event of adverse business, financial, or
            economic conditions, it is not likely to have the capacity to pay
            interest and repay principal. The "CCC" rating category is also used
            for debt, subordinated to senior debt, that is assigned an actual or
            implied "B" or "B-" rating.

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 that are 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 that are 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. These issues may be
            in default, or 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.


                                       13
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                             Statement of Assets and Liabilities
                                                                  March 31, 1998
================================================================================
<S>                                                               <C>          
ASSETS:
   Investments, at value (Cost-- $154,834,617) ............       $ 164,222,492
   Cash ...................................................                 114
   Interest and dividends receivable ......................           3,542,118
   Receivables for securities sold ........................             217,091
   Receivable for open forward foreign
      currency contracts (Note 11) ........................              38,594
                                                                  -------------
   Total Assets ...........................................         168,020,409
                                                                  -------------
LIABILITIES:
   Bank loan (Note 7) .....................................          30,000,000
   Payable for securities purchased .......................           1,152,694
   Investment advisory fees payable .......................             103,531
   Interest payable .......................................              91,692
   Administration fees payable ............................              40,889
   Accrued expenses .......................................             149,204
                                                                  -------------
   Total Liabilities ......................................          31,538,010
                                                                  -------------
Total Net Assets ..........................................       $ 136,482,399
                                                                  =============
NET ASSETS:
   Par value of capital shares ............................       $     152,021
   Capital paid in excess of par value ....................         127,193,454
   7% Cumulative Preferred Stock (Note 6) .................          30,000,000
   Undistributed net investment income ....................              72,651
   Accumulated net realized loss on
      security transactions ...............................         (30,361,341)
   Net unrealized appreciation on
      investments and foreign currencies ..................           9,425,614
                                                                  -------------
Total Net Assets ..........................................       $ 136,482,399
                                                                  =============
</TABLE>

<TABLE>
<CAPTION>
                                                        Per Share
                                                        ---------
NET ASSET VALUE, COMPRISED OF:
<S>                                                     <C>         <C>         
7% Cumulative Preferred Stock redemption value          $1,000.00   $ 30,000,000
Cumulative undeclared dividends on 7.00%
   Preferred Stock ...................................      20.71        621,366
                                                        ---------   ------------
Total allocated to Cumulative Preferred Stock ........  $1,020.71     30,621,366
                                                        =========   ------------
Common Stock (15,202,119 shares outstanding) .........  $    6.96    105,861,033
                                                        =========   ------------
TOTAL NET ASSETS .....................................              $136,482,399
                                                                    ============
</TABLE>

                       See Notes to Financial Statements.

                                       14
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                                         Statement of Operations
                                               For the Year Ended March 31, 1998
================================================================================
<S>                                                                 <C>        
INVESTMENT INCOME:
   Interest ....................................................    $15,620,488
   Dividends ...................................................        694,115
   Less: Interest expense (Note 7) .............................     (1,856,050)
                                                                   ------------
   Total Investment Income .....................................     14,458,553
                                                                   ------------

EXPENSES:
   Investment advisory fees (Note 2) ...........................        818,462
   Administration fees (Note 2) ................................        327,385
   Shareholder communications ..................................        174,999
   Audit and legal .............................................         92,589
   Directors' fees .............................................         35,000
   Shareholder and system servicing fees .......................         26,180
   Listing fees ................................................         24,800
   Pricing .....................................................         20,735
   Custody .....................................................          7,198
   Other .......................................................         16,701
                                                                   ------------
   Total Expenses ..............................................      1,544,049
                                                                   ------------
Net Investment Income ..........................................     12,914,504
                                                                   ------------
REALIZED AND UNREALIZED GAIN ON INVESTMENTS
AND FOREIGN CURRENCIES (NOTES 3 AND 11):
   Realized Gain From:
      Security transactions (excluding short-term securities) ..      1,634,699
      Foreign currency transactions ............................         82,326
                                                                   ------------
   Net Realized Gain ...........................................      1,717,025
                                                                   ------------
   Change in Net Unrealized Appreciation of Investments and
   Foreign Currencies:
      Beginning of year ........................................      2,870,108
      End of year ..............................................      9,425,614
                                                                   ------------
   Increase in Net Unrealized Appreciation .....................      6,555,506
                                                                   ------------
Net Gain on Investments ........................................      8,272,531
                                                                   ------------
Increase in Net Assets From Operations .........................    $21,187,035
                                                                   ============
</TABLE>


                       See Notes to Financial Statements.

                                       15
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                             Statements of Changes in Net Assets
                                                   For the Years Ended March 31,
================================================================================
                                                       1998             1997
                                                 -------------    -------------
<S>                                                <C>              <C>        
OPERATIONS:
   Net investment income .....................     $12,914,504      $13,332,776
   Net realized gain .........................       1,717,025          939,501
   Increase in net unrealized appreciation ...       6,555,506          208,576
                                                 -------------    -------------
   Increase in Net Assets From Operations ....      21,187,035       14,480,853
                                                 -------------    -------------
DIVIDENDS PAID FROM
NET INVESTMENT INCOME TO:
   7.00% Cumulative Preferred Stock ..........      (2,100,000)      (2,100,000)
   Common Stock ..............................     (11,728,952)     (10,475,099)
                                                 -------------    -------------
   Decrease in Net Assets From
      Distributions to Shareholders ..........     (13,828,952)     (12,575,099)
                                                 -------------    -------------
FUND SHARE TRANSACTIONS (NOTE 8):
   Net value of shares issued for
      reinvestment of dividends ..............       3,448,238        3,452,357
                                                 -------------    -------------
   Increase in Net Assets From
      Fund Share Transactions ................       3,448,238        3,452,357
                                                 -------------    -------------
Increase in Net Assets .......................      10,806,321        5,358,111
NET ASSETS:
   Beginning of year .........................     125,676,078      120,317,967
                                                 -------------    -------------
   End of year* ..............................    $136,482,399     $125,676,078
                                                 =============    =============
*  Includes undistributed net investment
      income of: .............................         $72,651         $911,910
                                                 =============    =============
</TABLE>


                       See Notes to Financial Statements.

                                       16
<PAGE>
 
<TABLE>
<CAPTION>
[GRAPHIC]
                                                                              Statement of Cash Flows
                                                                                   For the Year Ended
                                                                                       March 31, 1998
=====================================================================================================
<S>                                                               <C>                   <C>
NET DECREASE IN CASH:
Cash Flows Provided By Operating
   and Investing Activities:
   Interest and dividends received ..........................     $  14,250,096
   Operating expenses paid ..................................        (1,476,457)
   Interest payments on bank loans ..........................        (1,843,350)
   Purchases of short-term securities, net ..................         1,238,000
   Purchases of long-term securities ........................      (126,332,305)
   Proceeds from disposition of long-term securities ........       124,544,633
                                                                  -------------
   Net Cash Provided By Operating and
     Investing Activities ...................................                           $  10,380,617
                                                                                        -------------
Cash Flows Used By Financing Activities:
   Cash dividends paid on 7.00% Cumulative
     Preferred Stock ........................................        (2,100,000)
   Net cash dividends paid on Common Stock* .................        (8,280,714)
                                                                  -------------
   Net Cash Used By Financing Activities ....................                             (10,380,714)
                                                                                        -------------
Net Decrease in Cash ........................................                                     (97)
Cash--Beginning of Year .....................................                                     211
                                                                                        -------------
Cash--End of Year ...........................................                           $         114
                                                                                        =============
RECONCILIATION OF INCREASE IN NET ASSETS
FROM OPERATIONS TO NET CASH PROVIDED
BY OPERATING AND INVESTING ACTIVITIES:
Increase in Net Assets From Operations ......................                           $  21,187,035
   Amortization of discount on securities ...................        (2,325,434)
   Increase in investments ..................................       (11,388,401)
   Decrease in receivable for securities sold ...............         1,582,972
   Increase in payable for securities purchased .............         1,152,694
   Decrease in dividends and interest receivable ............            91,458
   Increase in accrued expenses .............................            80,293
                                                                  -------------
   Total Adjustments ........................................                             (10,806,418)
                                                                                        -------------
Net Cash Provided By Operating and Investing Activities .....                           $  10,380,617
                                                                                        =============
</TABLE>

*    Exclusive of dividend reinvestment of $3,448,238.


                       See Notes to Financial Statements.


                                       17
<PAGE>
 
[GRAPHIC]
                                                   Notes to Financial Statements
================================================================================

     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 


                                       18
<PAGE>
 
[GRAPHIC]
                                                   Notes to Financial Statements
                                                                     (continued)
================================================================================
and December 15; (h) the net asset value of the Fund's Common Stock is
determined no less frequently than the close of business on the Fund's last
business day of each week (generally Friday). It is determined by dividing the
value of the net assets available to Common Stock by the total number of shares
of Common Stock outstanding. For the purpose of determining the net asset value
per share of the Common Stock, the value of the Fund's net assets shall be
deemed to equal the value of the Fund's assets less (1) the Fund's liabilities
(including the outstanding principal amount on the bank loan), (2) the aggregate
liquidation value (i.e., $1,000 per outstanding share) of the 7.00% Cumulative
Redeemable Preferred Stock and (3) accumulated and unpaid dividends on the
outstanding Cumulative Redeemable Preferred Stock issue; (i) the Fund intends to
comply with the requirements of the Internal Revenue Code of 1986, as amended,
pertaining to regulated investment companies and to make distributions of
taxable income sufficient to relieve it from substantially all Federal income
and excise taxes; (j) the character of income and gains to be distributed are
determined in accordance with income tax regulations which may differ from
generally accepted accounting principles. At March 31, 1998, reclassifications
were made to the Fund's capital accounts to reflect permanent book/tax
differences and income and gains available for distributions under income tax
regulations. Net investment income, net realized gains and net assets were not
affected by this change; and (k) estimates and assumptions are required to be
made regarding assets, liabilities and changes in net assets resulting from
operations when financial statements are prepared. Changes in the economic
environment, financial markets and any other parameters used in determining
these estimates could cause actual results to differ.

     2.   Advisory Agreement and Transactions with Affiliated Persons

     Mutual Management Corp. ("MMC"), a subsidiary of Salomon Smith Barney
Holdings Inc. ("SSBH"), acts as investment adviser to the Fund. The Fund pays
MMC a management fee calculated at an annual rate of 0.50% of the average daily
net assets (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.


                                       19
<PAGE>
 
[GRAPHIC]
                                                   Notes to Financial Statements
                                                                     (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 year ended March 31, 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                                                           $127,484,999
--------------------------------------------------------------------------------
Sales                                                                122,773,131
--------------------------------------------------------------------------------
</TABLE>

     At March 31, 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                                        $9,585,135
Gross unrealized depreciation                                          (197,260)
-------------------------------------------------------------------------------
Net unrealized appreciation                                          $9,387,875
-------------------------------------------------------------------------------
</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 



                                       20
<PAGE>
 
[GRAPHIC]
                                                   Notes to Financial Statements
                                                                     (continued)
================================================================================
agreements to resell the securities to the sellers at a future date (generally,
the next business day) at an agreed upon higher repurchase price. The Fund
requires continual maintenance of the market value of the collateral in amounts
at least equal to the repurchase price.

     6.   Cumulative Redeemable Preferred Stock

     On March 16, 1993, the Fund issued 30,000 shares of 7.00% Cumulative
Preferred Stock, which will be redeemed in full on April 15, 2000, at a price
equal to $1,000 per share, plus accumulated and unpaid dividends. At March 31,
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 $621,366 at March 31, 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, 1998. Interest expense
related to the loan for the year ended March 31, 1998 was $1,856,050.

     8.   Common Stock

     At March 31, 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>
                                    Year Ended                  Year Ended
                                  March 31, 1998              March 31, 1997
                               ---------------------       ---------------------
                                Shares      Amount          Shares      Amount
--------------------------------------------------------------------------------
<S>                            <C>        <C>              <C>        <C>       
Shares issued on
   reinvestment                460,479    $3,448,238       516,581    $3,452,357
--------------------------------------------------------------------------------
</TABLE>


                                       21
<PAGE>
 
[GRAPHIC]
                                                   Notes to Financial Statements
                                                                     (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 March 31, 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
-----------------------------------------------------------------------------------------
<S>                                   <C>         <C>             <C>         <C>       
To Sell:                                                                     
British Pound                         249,075     $  415,936      5/26/98      $      809
European Currency Unit                281,048        303,181      6/18/98           4,417
German Mark                         3,330,616      1,807,471       6/2/98          33,368
-----------------------------------------------------------------------------------------
Total Unrealized Gain on Forward                                             
    Foreign Currency Contracts                                                 $   38,594         
-----------------------------------------------------------------------------------------
</TABLE>

                                       22
<PAGE>
 
[GRAPHIC]
                                                            Financial Highlights
================================================================================
Contained below is per share operating performance data for a share of common
stock outstanding, total return and ratios to average net assets based on Common
Shares outstanding. This information has been derived from information provided
in the financial statements and market price data for the Fund's shares.

For a share of common stock outstanding throughout each year:

<TABLE>
<CAPTION>
                                                          1998           1997           1996
                                                      -----------     ----------     ----------
<S>                                                      <C>             <C>            <C>    
Net Asset Value, Beginning of Year ................         $6.45          $6.31          $5.88
                                                      -----------     ----------     ----------
Income From Operations:
   Net investment income ..........................          0.87           0.92           0.86
   Net realized and unrealized gain ...............          0.56           0.08           0.45
                                                      -----------     ----------     ----------
   Total Income From Operations ...................          1.43           1.00           1.31
                                                      -----------     ----------     ----------
Distributions:
   Dividends declared to 7.00% Cumulative Preferred
      Stockholders ................................         (0.14)         (0.14)         (0.15)
   Dividends paid from net investment income ......         (0.78)         (0.72)         (0.73)
                                                      -----------     ----------     ----------
   Total Distributions ............................         (0.92)         (0.86)         (0.88)
                                                      -----------     ----------     ----------
Net Asset Value, End of Year ......................         $6.96          $6.45          $6.31
                                                      ===========     ==========     ==========
Market Value, End of Year .........................         $7.50          $7.25          $7.00
                                                      ===========     ==========     ==========
Total Return, Based on Market Value ...............         14.81%         15.55%         18.35%
                                                      ===========     ==========     ==========
Total Return, Based on Net Asset Value* ...........         19.75%         14.04%         20.01%
                                                      ===========     ==========     ==========
Net Assets**, End of Year (000's) .................      $105,861        $95,034        $90,318
                                                      ===========     ==========     ==========
Ratios to Average Net Assets Based on
Common Shares Outstanding+:
   Net Investment Income ..........................         12.60%         14.35%         14.21%
   Interest Expense ...............................          1.81           1.92           1.98
   Other Expenses .................................          1.51           1.59           1.65

Portfolio Turnover Rate ...........................            79%           101%            87%
</TABLE>
----------
*    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, 1997 and 1996 have been recalculated to reflect this
     methodology.

                                       23
<PAGE>
 
[GRAPHIC]
                                                Financial Highlights (continued)
================================================================================
For a share of common stock outstanding throughout each year:

<TABLE>
<CAPTION>
                                                          1995          1994#
                                                      ----------     ----------
<S>                                                      <C>            <C>    
Net Asset Value, Beginning of Year ................        $6.76          $6.86
                                                      ----------     ----------
Income From Operations:
   Net investment income ..........................         0.93           1.02
   Net realized and unrealized loss ...............        (0.78)         (0.13)
                                                      ----------     ----------
   Total Income From Operations ...................         0.15           0.89
                                                      ----------     ----------
Distributions:
   Dividends declared to 7.00% Cumulative Preferred
      Stockholders ................................        (0.16)         (0.11)
   Dividends declared to 9.67% Cumulative Preferred
      Stockholders ................................           --          (0.12)
   Dividends paid from net investment income ......        (0.87)         (0.82)
   Change in accumulated undeclared dividends on
      Preferred Stock .............................           --           0.06
                                                      ----------     ----------
   Total Distributions ............................        (1.03)         (0.99)
                                                      ----------     ----------
Net Asset Value, End of Year ......................        $5.88          $6.76
                                                      ==========     ==========
Market Value, End of Year .........................        $6.63          $7.13
                                                      ==========     ==========
Total Return, Based on Market Value ...............         6.41%         10.02%
                                                      ==========     ==========
Total Return, Based on Net Asset Value* ...........        (0.53)%        10.24%
                                                      ==========     ==========
Net Assets**, End of Year (000's) .................      $80,309        $87,726
                                                      ==========     ==========
Ratios to Average Net Assets Based on
Common Shares Outstanding:
   Net Investment Income ..........................        15.35%         14.38%
   Interest Expense ...............................         1.58           0.92
   Other Expenses .................................         1.65           1.60
Portfolio Turnover Rate ...........................           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.

                                       24
<PAGE>
 
[GRAPHIC]
                                                    Independent Auditors' Report
================================================================================
The Shareholders and Board of Directors of
Zenix Income Fund Inc.:

     We have audited the accompanying statement of assets and liabilities,
including the schedule of investments, of the Zenix Income Fund Inc. as of March
31, 1998, and the related statement of operations for the year then ended, the
statements of changes in net assets for each of the years in the two-year period
then ended, the statement of cash flows for the year then ended, and the
financial highlights for each of the years in the three-year period then ended.
These financial statements and financial highlights are the responsibility of
the Fund's management. Our responsibility is to express an opinion on these
financial statements and financial highlights based on our audits. The financial
highlights for each of the years in the two-year period ended March 31, 1995
were audited by other auditors whose report thereon, dated May 12, 1995,
expressed an unqualified opinion on those financial highlights.

     We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements and financial
highlights are free of material misstatement. An audit includes examining, on a
test basis, evidence supporting the amounts and disclosures in the financial
statements. Our procedures included confirmation of securities owned as of March
31, 1998, by correspondence with the custodian. As to securities purchased or
sold but not yet received or delivered, we performed other appropriate auditing
procedures. An audit also includes assessing the accounting principles used and
significant estimates made by management, as well as evaluating the overall
financial statement presentation. We believe that our audits provide a
reasonable basis for our opinion.

     In our opinion, the financial statements and financial highlights referred
to above present fairly, in all material respects, the financial position of the
Zenix Income Fund Inc. as of March 31, 1998, and the results of its operations
for the year then ended, the changes in its net assets for each of the years in
the two-year period then ended, its cash flows for the year then ended and its
financial highlights for each of the years in the three-year period then ended,
in conformity with generally accepted accounting principles.

                                            KPMG Peat Marwick LLP

New York, New York
May 15, 1998

                                       25
<PAGE>
 
[GRAPHIC]
                                         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       1997       1996       1995       1994
                                          --------   --------   --------   --------   --------
<S>                                       <C>        <C>        <C>        <C>        <C>     
7.00% Cumulative Preferred Stock (1)
  Total amount outstanding (000s)         $ 30,000   $ 30,000   $ 30,000   $ 30,000   $ 30,000
  Asset Coverage Per Share                   2,760      2,580      2,490      2,439      2,583
  Involuntary Liquidating Preference
    Per Share (2)                            1,000      1,000      1,000      1,000      1,000
  Average Market Value Per Share (2)(3)      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         --         --
  Asset Coverage (000s)                    165,900    154,800    149,400         --         --
</TABLE>
----------

(1)  Redeemable April 15, 2000.
(2)  Excludes accrued interest or accumulated undeclared dividends.
(3)  See Note 6.

                                       26
<PAGE>
 
[GRAPHIC]
                                     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
</TABLE>
----------
*    Per share of Common Stock.



                                       27
<PAGE>
 
[GRAPHIC]
                                                      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>   
        4/23/96        4/26/96        $6.875         $6.27          $0.060          $6.531
        5/28/96        5/31/96         6.875          6.33           0.060           6.531
        6/25/96        6/28/96         6.750          6.22           0.060           6.413
        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
=============================================================================================
</TABLE>
*    As of record date

                                        28
<PAGE>
 
[GRAPHIC]
                                                      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>
 
[GRAPHIC]
                                                      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>
 
[GRAPHIC]
                                                      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 90 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 90 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>
 
[GRAPHIC]


                                                     Tax Information (unaudited)
================================================================================

     For Federal tax purposes the Fund hereby designates for the fiscal year
ended March 31, 1998:

     o    4.99% of the ordinary dividends paid as qualifying for the corporate
          dividends received deduction.

     o    A total of 1.59% of the ordinary dividends paid by the Fund from net
          investment income are derived from Federal obligations and may be
          exempt from taxation at the state level.


                                       32
<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.

                                  FD02395 5/98

================================================================================