Geico Corp. reported slight increases in third-quarter and nine-month profits over levels for the comparable periods of 1978.

Profits for the nine-month period were $61.8 million ($2.17 per fully diluted share), compared to $61.5 million ($1.74) for the same period last year.

For the quarter ending Sept. 30, Geico reported profits of $21.4 million (84 cents), up from $20 million (57 cents) for the third quarter in 1978.

Geico's nine-month operating income, excluding capital transactions, totaled $46 million ($1.61), up 4 percent over the $44.1 million ($1.23) reported for the same period last year.

The company said its subsidiary, Government Employees Insurance Co., had a "modest." Increase in written premiums for the nine months, with those figures rising from $443.3 million in 1978 to $473.4 million this year.

Geico Corp. Chairman John J. Byrne said the company is "growing slowly" and said that "on balance, the year continues to go reasonably well for us."

Byrne called the performance by its automobile insurance subsidiary "satisfactory," noting that the underwriting ratio dropped to 94.5 percent for the first nine months of the year from 96.4 percent last year.

Bryne said that a decline in the insurance underwriting cycles primarily has affected the property casualty field.

But byrne also said that the costs of repairing customers' automobiles are "increasing at rates substantially above the general level of inflation."

In other reports, W. Bell & Co. reported a slight increase in profits for the quarter ending Sept. 29 to $81,700 (8 cents) from $77,300 (8 cemts).

The chain, with 12 stores in Maryland, Virginia, the District and Texas, reported a 45 percent sales increase for the quarter totaling $15.8 million, up from $10.9 million last year.

Black & Decker Manufacturing Co. said total profits for its fiscal year ending Sept. 30 were $94.4 million ($2.25) compared to $66.2 million ($1.58) for the previous year.

For the quarter ending Sept. 30, Black & Decker reported profits of $29.5 million, nearly doubling last year's profits of $15.4 million for the same period.

Financial Security Group Inc. yesterday reported a drop in profits for the third quarter. The casualty insurance holding company of International Bank said quarterly profits were $2.8 million (92 cents) compared to $3.5 million ($1.18) last year.

Financial Security said its profits for the first nine months of 1979 totaled $7.5 million ($2.51), compared to $8.1 million ($2.69) last year.

The company attributed its profits decline to underwriting losses from storms, particularly hurricanes, and to increased automobile losses.