First Virginia Bankshares Corp., a bank holding company based in Falls Church, yesterday reported record profits for the second consecutive quarter.

The company, which owns one of the largest banking systems in Northern Virginia, listed profits before securities transactions in this year's third quarter of $2.63 million (25 cents a share) compared with $2.2 million (21 cents) in the same period last year, a gain of 20 per cent. Net income substantially was the same in both quarters.

For the first nine months, First Virginia earned a record $7.15 million (68 cents) compared with $6.3 million (60 cents) a year earlier. Net income rose 24 per cent to $7.8 million (74 cents) vs. $6.3 million (60 cents).

Chairman Ralph A. Beeton said deposit and loan growth experienced by First Virginia banks in the first two quarters of the year continued through Sept. 30, when deposits totaled [WORD ILLEGIBLE] million (up 12 per cent).

Last month, a three-judge panel of the U.S. Court of Appeals for the Fifth Circuit unanimously upheld a 1975 judgment awarding the banking firm damages of $1 million against previous owners of the former Benson Investment Corp., a consumer finance firm that had been acquired by First Virginia in 1973.

Avemco Corp., a Bethesda firm whose principal subsidiary is engaged in aircraft insurance, reported third-quarter profits of $643,490 (24 cents a shares) compared with $387,217 (13 cents) in the same period last year. Revenues rose to $3.6 million form $3.2 million.

That brought nine-month profits to $1.7 million (58 cents) vs. $1.5 million (50 cents) as revenues climbed to $10.4 million from $9.9 million.

Atlantic Research Corp., of Alexandria, reported profits of $689,000 ($1.44 a share) in the first nine months of 1977, up sharply from $273,000 in the comparable period last year. Sales rose to $24.6 million from $18.7 million.

The company, for which year-earlier pre-share earnings were not available, attributed its gains to development and marketing of new products and several government contracts.