Three former Navy officers were found innocent yesterday of charges that they had conspired to induce the Iranian Navy to sign a training contract with a private company in which they had an interest.

A U.S. District Court jury in Alexandria acquitted Malcolm W. Cagle, 59, a retired three-star admiral of Lynchburg, Va. James N. Hooper, 54, of Pensacola, Fla., a retired captain and Cagle's deputy and Dominic A. Paolucci, 54, of Alexandria, a retired Navy captain, of charges that they had defrauded the American government concealed the scheme.

The jury deliberated for 6 1/2 hours before returning a verdict. Moments later, Cagle said, "I knew I was innocent, but I also knew I would be vindicateo." Hooper and Paolucci also said they had been confident all along they would be acquitted.

The prosecution charged that Paolucci, former president of Lulejian and Associates, Inc., a defense contrator, had offered Cagle and Hooper jobs in return for their help in getting the company a contract to train 2,000 Iranian officers and enlisted men.

Had they been convicted on all counts, Hooper and Cagle would have received maximum sentences of 12 years in prison and a $30,000 fine, or both.Paolucci, charged only with conspiracy, would have received a maximum sentence of five years in prison or a $10,000 fine or both.

Much of the testimony during the complex trial concerned the key issue of whether Hooper Cagle had told the Navy everything they planned to do on a trip to Iran.

Ret. Rear Adm. Harold A. Gerhard, the man to whom they were required to report any proposals they planned to make or did make to officials of the Iranian Navy, testified that Hooper had not mentioned in a briefing that he and Cagle intended to recommend Lulejian as the contractor for the training project.

"You have nothing in your hip pocket?" Gerhard testified as having asked Hooper after the briefing. The response, according to Gerhard, was "No."

Cagle, the Navy's former chief of training and education, testified during the trial that he had in fact recommended to the then-commander of the Imperial Iranian Navy that he sign with Lelejian. But Cagle added that he had done so only after he had been asked to recommend a specific company Cagle added that he had previously mentioned about 10 American firms capable of carrying out the training.

Cagle, who served 37 years in the U.S. Navy and has written six books on Navy training and the Navy's role in World War II and Korea, also said that although he recommended Lulepian for the contract work, he had not presented the Iranian government with a detailed plan the company had prepared on the issue because he did not think it would be proper.

Cagle's attorney, Brain P. Gettings, argued repeatedly to the jury during the trial that his client had many job offers after retiring from the Navy and did not need a job with Lulejian.

Responding to questions from Gettings, Cagle testified that he had earned $108,000 in 1975 from consulting work and his $30,000-a-year Navy pension as well as other projects.

Cagle retired from the Navy in August, 1974.

"As of July, 1975, you weren't exactly scrambling for a job, were you?" Gettings asked.

Hooper claimed that he had made no retirement plans before he left the Navy in August, 1974, because his mother was ill and he wanted to see how her health held up. In addition, Hooper said, he had decided to take a part-time job only, and one that would not require him to travel much from his new home in Pensacola, Fla.

Hooper also said he did not know that Cagle, in two letters to Lt. Gen. Dvol Brett, then the head of the U.S. military advisory group in Iran, had mentioned that Hooper had agreed to join Lulejain. The two letters were written by Cagle in July, 1974, more than a month before the two men retired from the Navy.

The prosecution concentrated on the two letters and based much of its case against the three men on them. In the letters, Cagle also told Brett that he would direct a Lulejian board of advisors, which he was setting up to oversee the Iranian training program.

The crux of Paolucci's defense was that altough he was the president of Lulejian at the time the men allegedly conspired to defraud the government, he had not hired Hooper and Cagle and had in fact no authority to do so.

Paolucci said he had first learned of the job offer to Cagle in August, 1974, during a conversation with Cagle, and added that he had immediately telephoned retired Air Force Col. Norai Lulejian, the company's board chairman, to find out what was going on.

Cagle turned down Lulejian's first offer, according to the defensee, but went to work for the company one month after leaving the Navy in 1974.

Paolucci said that Col. Lulejian had been very impressed by Hooper and had asked that he be hired. Paolussi said he interviewed Hooper in August, 1974 for a job, well after Hooper had submitted his resignation to the Navy, Hooper, like Cagle, joined Lulejian shortly after he left the Navy.

Paolucci's testimony was contradicted in a deposition filed in the case by Col. Lulejian. In that deposition, taken in California because of the colonel's ill health, Lulejian testified that in June, 1974, Paolucci told him the company should hire Cagle, and if they did so, Lulejian would have a good chance of being awarded the contract. Lulejian also said he had written Cagle a letter offering him a consulting job at Paolucci's request.