Four Arlington deputies challenging their recent demotions in court said they did not know that their names would be used in a political advertisement that criticized Sheriff James A. Gondles Jr. for mismanagment and abuse of power, according to testimony in the case.

Last month Gondles gave the deputies the option of being demoted to the department's lowest position or being fired, saying at the time he no longer had confidence in their ability to perform their jobs because they had criticized him publicly and because he had received reports that they were engaging in activity disruptive to the office.

The four, who brought suit against Gondles in U.S. District Court arguing that the action violated their constitutional rights of free speech, said in depositions obtained Thursday that they had given written permission to the sheriff's opponent, Ronald B. Hager, to use their names in the campaign but had not seen the political mailer before it was published.

They expressed dissatisfaction with the wording and tone of the letter, which said, in part, that challenger Hager was in the race to "expose the mismanagement and abuse of power by Gondles" and would "restore integrity and no-nonsense to that office."

The statement included the signatures of 21 deputies, which Hager said he obtained when each signed a release form giving him permission to use their names in his campaign.

"I was annoyed when I saw this," said deputy Richard Tanner in his deposition, "and I thought, oh man . . . they're trying to say that we're all saying there's mismanagement and abuse of power, and that is not what I was saying."

Yesterday Hager said, "They authorized the use of their names. I don't think it's misleading to anyone," adding that he did not show the deputies the statement before it was published in an effort to keep it secret as long as possible.

"I don't feel the literature insinuated that they were attacking the sheriff's credibility . . . . They were supporting me," said Hager.

Gondles, a Democrat, won reelection to a third term after a sometimes bitter campaign against Hager, his former chief deputy who ran as a Republican-backed independent.

Gondles said in his sworn testimony that he concluded the four deputies were being disruptive based on verbal reports by other deputies. He said he had not conducted a formal investigation into those statements, which is done often when accusations are made about a deputy's conduct.

The allegations, he said, were made by his chief deputy, Thomas Faust, and by numerous other deputies, all of whom supported him during the campaign.

"I had more than one manager . . . telling me that the office and the operations of the office was being disrupted by these individuals, that they weren't willing to or could not, for whatever reasons, work with their supervisors or with other supervisors in carrying out the policies of the Sheriff's office," Gondles said in his statement. ". . . I am convinced that that information is correct."

The disruptive behavior cited by Gondles and Faust, who also gave a deposition, included such things as receiving too many personal phone calls and expressing discontent about the election and the sheriff's handling of certain personnel matters.