WASHINGTON - The resurgence of consumer demand for fixed-rate loans once again fueled strong earnings at Fannie Mae and Freddie Mac in the third quarter.

Earnings at Fannie Mae jumped 10% to $596.8 million. At Freddie Mac, earnings rose 12% to $278 million.

Both agencies also reported increases over second-quarter levels, reflecting the continued shift of consumers from adjustable-rate mortgages to fixed-rate loans this year.

At Fannie Mae, earnings rose about 4% from the second quarter. At Freddie Mac, earnings climbed about 5%.

Fannie Mae and Freddie Mac took advantage of the ample supply of fixed- rate loans and the slightly wider net interest margin to build their loan portfolios. The increased supply of fixed-rate loans meant that the agencies could purchase the loans at better prices.

The cost of debt used to finance mortgage purchases was also down slightly, according to Michael McCabe, director of shareholder relations at Freddie Mac.

By the end of the third quarter, Fannie Mae's portfolio stood at $240 billion, up $9.6 billion from the previous quarter. Freddie Mac's portfolio grew by $9.5 billion over the third quarter to reach $95 billion.

These portfolios provided much of the earnings growth at Fannie Mae and Freddie Mac.

Net interest income at Fannie Mae, which consists mostly of earnings on the mortgage portfolio, was $777.5 million, up 7% from the same period last year, and up about 8% from the second quarter.

At Freddie Mac, net interest income was $368 million, up 30% from the same period last year, and up 14% from the second quarter.

Gary J. Gordon, an analyst at PaineWebber Inc., New York, said both agencies have adopted a long-term strategy of building their mortgage portfolios, because they are looking for a way to invest large amounts of capital.

While mortgages in the portfolio yield higher returns than the securitized mortgages, returns on equity for the two lines of business are comparable, Mr. Gordon said. That's because the agencies have to hold about six times as much capital against the mortgages they buy as on those they securitize, he said.

Between them, Fannie Mae and Freddie Mac have about $2.65 billion in earnings to reinvest this year, Mr. Gordon said. The portfolio business can absorb more of this capital than the mortgage-backed securities business, he said.

Results on guarantee fee income were more mixed in the third quarter. At Fannie Mae, guarantee fees were $271.8 million, down about 1% from the same period last year, but up 2% from the second quarter.

At Freddie Mac, guarantee fee income was $270 million, down 4% from the same quarter last year, and down 0.7% from the second quarter. But Freddie's chairman, Leland Brendsel, promised that the agency's securitization business would grow as mortgage volumes increased.

Other income, which at both agencies reflects income from converting securities to real estate mortgage investment conduits or Remics, was down at Fannie Mae and up at Freddie Mac, compared with the third quarter of 1994.

Miscellaneous income was $22.4 million at Fannie Mae, against $28.6 million for the same period last year. It was $7 million at Freddie Mac, against $6 million for the third quarter of 1994.

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