The daughter of admitted spy John Anthony Walker Jr. testified today that when her father discovered that her husband knew of his espionage activities, "He asked me how much I cared about my husband and how I would feel if he suddenly no longer existed."

Asked her reaction to her father's implicit threat, Laura Mae Walker Snyder responded, "I said I didn't care."

Snyder, who was an Army communications specialist during 1978-79, said her father tried "many, many times" to persuade her to spy for him.

"He told me that the offer was always open, that it would never be closed," said Snyder, 26, the third of Walker's four children.

Snyder is now obtaining a divorce from her husband, Phillip Mark Snyder of Laurel. She has said her estranged husband "blackmailed" her, threatening to expose her father's espionage if she tried to regain custody of their son from him. Phillip Snyder has denied making such a threat.

Ultimately Laura Snyder and her mother, Barbara Joy Crowley Walker, tipped the FBI to John Walker's spying. Barbara Walker said at a news conference after her testimony Monday that Phillip Snyder's threats prompted them to call the FBI.

Snyder's testimony came in the espionage trial of retired Navy communications expert Jerry Alfred Whitworth, John Walker's former close friend and Navy colleague.

She said that in 1982, a few weeks after she left her husband, Whitworth lent her $600, which she has not repaid.

"It seemed to me that Mr. Whitworth was in a position to loan money to me," she testified. "He had nice cars and nice furniture and it seemed to me he had money to buy whatever he wanted."

Whitworth allegedly received $332,000 for his role in the espionage ring, which also included John Walker's son, Navy Seaman Michael Lance Walker.

In other testimony today, John Walker's brother, retired Navy Lt. Cmdr. Arthur James Walker, 51, who was convicted of espionage last August, testified that his brother told him about "his man on the West Coast" who was supplying crypto-graphic information that he photographed in a van bought by John Walker's "buyer."

However, U.S. District Judge John P. Vukasin Jr. barred Arthur Walker from testifying that his brother had told him the supplier's first name was "Jerry."

Whitworth, 46, the last of four Navy men charged in the Walker case to face trial, is accengineering position the next month at VSE Corp., a Chesapeake, Va., defense contractor, his brother asked whether he had access to classified material.

Although he had originally understood that the information was being supplied to private organizations such as the publication, "Jane's Fighting Ships," Arthur Walker testified, he said John Walker's request for classified material "just seemed to indicate . . . certain people now would be interested in classified information -- other countries."

Arthur Walker was found guilty of seven counts of espionage Aug. 9 by a federal judge in Norfolk. He gave his brother portions of two documents marked "confidential," the lowest category of classified information.

He testified that John Walker stepped up the pressure on him to supply classified information in 1982 and again in 1983, telling him that his West Coast supplier was planning to retire from the Navy. Whitworth retired from the Navy in October 1983.

Arthur Walker denied engaging in any espionage before he was recruited by his brother in January 1980, and said Barbara Walker did not tell him about John Walker's spying in 1968. Barbara Walker testified earlier this week that when she confided in her brother-in-law about John Walker's espionage, Arthur Walker told her he had engaged in spying in 1968 while stationed at a submarine base in Groton, Conn.