Annapolis-based Farmers National Bancorp, the oldest banking company in Anne Arundel County, is officially on the block.

The company, which has $709 million in assets and 20 branches, announced yesterday it has received takeover proposals from two companies. It declined to reveal the names of the suitors.

First Virginia Banks Inc., which owns a bank in Virginia and two banks in Maryland, was named as one of the suitors by the Annapolis Capital yesterday.

"As a policy we don't comment one way or the other" on takeover rumors, said Thomas P. Jennings, vice president and general counsel for First Virginia.

Farmers National, founded in 1805, is the parent of Farmers National Bank of Maryland, the Caroline County Bank and Atlantic National Bank in Ocean City.

In the last two weeks the company's stock, which normally trades thinly in a narrow range, has moved up more than 11

percent. It closed unchanged yesterday at $38.50 a share.