Two suspects in separate Arlington bank robberies, in one of which a 62-year-old customer was shot to death, are being held on Long Island, N.Y., where they were arrested Dec. 13 on charges of possessing a stolen car, police reported yesterday.

Nassau County, N.Y., police said they learned after an investigation that included a computer check earlier this week that the men, taken into custody after allegedly found driving a car stolen from the District of Columbia, are wanted in the Arlington holdups.

One man, Luther Tomlinson, 19, of Elmont, N.Y., is wanted in the Nov. 22 robbery of a First Virginia Bank branch in the Shirlington Shopping Center in which Robert Jennings was slain. Jennings, a construction company foreman from Northeast Washington, went to the bank to deposit the first paycheck he had been able to pick up himself since recovering from colon cancer surgery.

Nassau County police said they believe that Tomlinson is suspected of driving a car used to escape from the holdup scene.

The bank branch, which had had three other robberies in the three previous months, closed because of the frequent hold-ups.

The other man, Julian Holmes, 34, of Queens, N.Y., is wanted in another Arlington bank robbery Sept. 14, Nassau County police said.