When Alexandria Mayor James P. Moran Jr. displayed a model helicopter at Saturday's City Council meeting, he could have been illustrating the influence of his predecessor and political rival, Charles E. Beatley.

Although Moran defeated Beatley for mayor in May, knocking him out of a position he had held for 15 years, it appeared from last week's dispute over a proposed heliport that Moran's battles with Beatley are far from over.

"It's the first thing you've ever given me," Moran said, amid chuckles as he cradled the tiny helicopter Beatley had presented him.

Beatley, 68, a retired airline pilot, quickly replied that the new mayor, a 39-year-old stockbroker who opposes the heliport, could not keep the model.

"Apparently, he has some influence," Moran said about Beatley this week. "It looks like he has the votes to pass the heliport." Then he added: "Obviously, he isn't going to influence my vote."

Moran stressed that there were still 60 days before the council has to decide whether to approve the construction of a landing and parking site for as many as six helicopters near the Eisenhower Avenue Metro station. Within that time, he said, he and council member Carlyle C. Ring, who both voted recently to table the project, might be able to get two more votes on the seven-member council.

For Moran, Beatley's continued activism in Alexandria politics could turn out to be a constant tug-of-war with the man who went from mentor to political opponent.

Moran, a Democrat like Beatley, resigned from the council as part of a plea agreement on a conflict-of-interest charge in 1984 amid much criticism from Beatley. With their relationship soured, Moran challenged Beatley as an independent and won a contest that focused on criticism of the city police and Beatley's support of a grand jury investigation that produced many incriminations but no indictments.

Moran and Beatley have often taken opposing sides of issues, such as the Beatley-sponsored DASH bus system that Moran still refers to as "Chuck's toys." The mayor insists that his opposition has nothing to do with Beatley himself: "If he ever came up with a full-baked idea, I'd vote for it."

Even though federal and state funds are likely to pay 95 percent of the estimated $3 million heliport, Moran argues that unless the heliport is built on top of a high-rise, it would deny valuable land to the city's tax rolls. He also said it would likely benefit wealthy out-of-town executives and the helicopter industry more than it would Alexandrians.

Beatley, however, argued that Alexandria should be the site of the region's first public heliport and emphasized the importance of a future-looking facility that could shuttle executives and passengers to the now-booming Dulles International Airport.

"You're going to see business come to Alexandria, hotel business, that wouldn't have come without a heliport," Beatley said, enthusiastically supporting the heliport that Moran has called a "nutty idea."

Beatley also came to the council last month, that time to lead a Seminary Hills neighborhood chorus against the refinancing of a $10.46 million loan to Alexandria Hospital. Saying he began his political career around 1960 because he objected to the hospital's plans to build physicians' offices in the single-family home neighborhood, Beatley argued that the loan would aid the hospital's plans for an outpatient facility, cancer center and doctors' offices.

Although Beatley did not block the refinancing, he did prompt the council to say that not one cent of the money could be used for an expansion.

Pulling out first 22-year-old newspaper clippings chronicling citizen uproar over the hospital's plans and then his own typed arguments, single-spaced on five pages of legal-size paper and dated Feb. 13, 1963, Beatley seemed to command more attention from the council and audience than other speakers. Council members are reluctant to say how much, if any, influence the five-term former mayor has on council.

"I'm not answering that," said council member Redella (Del) Pepper, a former Beatley aide, when asked how much weight Beatley's testimony carries. "Where his influence really is, is with the people."

Beatley, himself, says he doesn't have as much influence on council as he has with residents, but he said, "It is they who turn around and make their representations to council."

Besides the heliport and the hospital, will Beatley be felt behind the scenes and in front of City Council in the new year?

"I said when I went out of office, I wouldn't go away," Beatley said, vowing to push the DASH system, which is now a 17-bus fleet, into a system with as many as 50 or 60 buses.

Then, asked what other issues he would like to address, Beatley was not at a loss for words. He would watch Moran, he said, on development "and transportation and density issues."