Financial General Bankshares, Inc., a holding company with banks in the District, Maryland and Virginia, reported yesterday that its third-quarter and nine-month earnings topped 1979 levels.

But American Management Systems of Arlington said its third-quarter earnings fell below last year's.

Financial General's third-quarter net income before securities transactions rose to $4.291 million (61 cents a share) from $3.741 million (54 cents) a year ago, while nine-month net was $11.564 million ($1.66) compared with $9.589 million ($1.38).

Earnings for the quarter and the year to date were records, giving the company a string of nine consecutive three-month periods of record profits, according to Chairman B. F. Saul ii and President J. William Middendorf ii.

Growth in all categories of loans outstanding and rising rates of interest -- principally in commercial lending -- were the main reasons for the continued strong performance, Middendorf said.

AMS said it earned $491,000 (33 cents a share) in this year's third quarter compared with $566,000 (50 cents) in the 1978 period.

A spokesman said the quarter last year was exceptionally strong, while this year's is below average due to a dispute with a client over changes in a major contract.

Third-quarter revenues, however, rose 38 percent to $13.169 million from $9.514 million, and both net income and revenues for the year to date showed improvements. Nine-month net income was $1.271 million (90 cents), up from $874,000 (78 cents), and revenues were 54 per cent higher at $35.131 million compared with $22.760 million.

Avemco Corp., a national aviation insurance and finance service firm with headquarters in Bethesda, had third-quarter net earnings of $754,000 (30 cents a share), up 80 percent over the $418,000 (17 cents) earned in the third quarter of 1978. Revenues rose from $4.7 million to $5.14 million.

The company's nine-month earnings of $2.4 million (97 cents) surpassed all previous records. Avemco earned $1.4 million (57 cents) in the first nine months of 1978. Revenues were $14.2 million, up from $11.76 million.

Avemco Chairman Arnold H. Johnson has expressed concern over a recent purchase of 131,800 shares of Avemco common stock by Associated Madison Companies Inc. "At such time as we may become aware of any attempt to gain control, we will evaluate such action from the point of view of stockholder's interest." Johnson said.

Atlantic Research Corp. of Alexandria reported that a court victory in a patent infringement lawsuit boosted the company's third quarter earnings ahead of the previous year. But operating income was down and earnings per share were off because more stock was sold in June.

Atlantic Research earned $336,000 (22 cents a share) for the quarter, up from $329,000 (29 cents a share) a year ago. The company said $132,000 of the latest quarter's earnings came from the court settlement, indicating operating income fell to $197,000. Sales by the solid fuel rocket and communications equipment maker climbed to $12.3 million from $9.9 million.

For the first nine months of the year, Atlantic Research showed net income of just over$1 million (85 cents), up from $954,000 (91 cents) and sales of $37.2 million, up from $31.4 million.

National Bank of Washington's net income increased to $1.76 million ($1.28 a share) from $1.34 million (98 cents), a 34 percent gain. Income before securities transactions increased to $1.76 million ($1.28) from $1.56 million ($1.14).

For the nine months, NBW reported income before securities dealings of $4.79 million ($3.49), up from $4.51 million ($3.28) and net income of $4.79 million ($3.49), up from $4.28 million ($3.12).

Bank of Columbia, N.A. showed income before securities transactions of $254,000 (58 cents) for the first nine months of the year, up 120 percent from the $115,000 (26 cents) earned a year ago.

Flow General Inc. reported a 49 percent increase in its first-quarter earnings over the same quarter last year on sales that were up to 29 percent.

The McLean firm earned $713,000 (41 cents a share) compared with $478,000 (30 cents) the previous year. Sales were $16.7 million versus $12.9 million in the first quarter of fiscal 1979.

First American Bank of Maryland reported its income before securities transactions for the third quarter increased to $683,000 (70 cents per share) from $594,000 (60 cents) and net income climbed to $643,000 (66 cents) from $577,000 (58 cents).

President G. J. Manderfield said profits of the Financial General affiliate bank increased primarily because the interest rates the bank charges for loans increased faster than the interest rates it pays on deposits.

For the first nine months of the year, First American earnings before securities transactions were up to $1.8 million ($1.85 per share) from $1.6 million ($1.63) and net profits increased to $1.7 million ($1.76) from $1.6 million ($1.61).

First American's directors declared the regular quarterly cash dividend of 16 cents per share to be paid Oct. 19 to stockholders as of Sept. 28.