When underwater explorer Jacques Cousteau agreed to move his Cousteau Society to Norfolk five years ago, city officials were delighted that they had managed to lure a world-renowned figure from New York with little more than the offer of an unused schoolhouse for his headquarters.

Cousteau's move to Virginia has been a happy one and has spawned plans for what his supporters say would be a unique ocean center, one that would draw thousands of tourists to the Norfolk waterfront with Disneyland-like copies of the underwater environments that have been the focus of Cousteau's successful television specials.

But there is a catch to the proposal: Norfolk is being asked to issue $15.5 million in general obligation bonds to support the center's construction.

That proposal has split the city's once tightly knit leadership as few issues have. Mayor Joseph A. Leafe has said he supports the project and will vote for it when the issue comes before the seven-member City Council for a final vote Tuesday.

A number of council members and some of the city's most influential businessmen don't. That has cast doubt on whether the French-born explorer will win what once seemed like a routine council vote.

"Captain Cousteau and the Cousteau Society deserve all the acclaim they have received for their research and dramatization of the problems of the sea," said Josh Darden, a leader of the opposition. "It does not necessarily follow, however, that they would be reliable, financially sound business partners for Norfolk . . . . "

Specifically, Darden and others, including two former mayors, are skeptical about whether the center's projected number of visitors -- 650,000 annually at $6.95 a head -- is realistic. Without that many visitors, the opponents say, city taxpayers would be obligated to pay the deficit on the city-backed bonds.

Darden also is upset that the Cousteau Society's permanent headquarters and a replica of Cousteau's research ship Calypso would not be included in the center under the initial plans. They are now, but that hasn't ended all the concerns.

Darden said the society should help to raise funds from the private sector to pay part of the center's $24.7 million overall cost and he recalled that a Cousteau-designed sea museum aboard the ocean liner Queen Mary in Long Beach, Calif., closed $12 million in debt after 10 years.

Cousteau supporters say the Cousteau Society only designed the Queen Mary museum and didn't operate it. Moreover, they noted that supporters are planning to help raise $3 million in the coming months to help finance the center. Mayor Leafe said the city will probably wait six months after Tuesday's vote to see if that money is raised before it issues any bonds.

The proponents express fear that the debate and high emotions the center has aroused not only will kill the project, but may have chilled the city's relationship with Cousteau.

While in Washington for his father's 75th birthday last month, Jean-Michel Cousteau, who works at the society office in Norfolk, said, "It seems like the right hand does not know what the left is doing down there. It's like a marriage. If the chemistry isn't right, you don't get married . . . . If they don't want it, the world is big."

"I don't know how . . . those seven individuals on the council will vote," said Charles Vinick, a vice president of the society, the nonprofit organization of 15,000 members devoted to the preservation of the oceans and pursuit of Cousteau's work. "I think it's close."

Cousteau's supporters reject the doubts about the visitors they are projecting, citing in part the 1 million visitors the Baltimore Aquarium drew in its first year.

Vinick said the center will be the only one of its type in the world. The society's negotiations for affiliated projects in other cities, such as Paris and St. Louis, do not include plans for the same kind of center or for the society's headquarters, he said.

Other critics have said they fear the center's appeal will decline after Cousteau's death. Tom Blanchard, executive director of the Norfolk Recreational Facilities Authority, a city agency that has spent more than $1 million in state and local funds on the project, rejects that criticism.

Cousteau "has endured and we believe that will continue," Blanchard told the Associated Press.

The center would open in the spring of 1988, if the council approves. It would be housed in a new 75-foot high cylindrical building on a three-acre peninsula known as "banana pier" after the old banana steamships that used to dock there.

Following Cousteau's opposition to the captivity of animals, the Center would not be an aquarium or a museum. It would offer a simulated space shot, followed by a walk down a spiral, descending ramp, passing numerous high-technology exhibits offering experiences of the sea's mysteries at varying depths until the ocean floor is reached. A restaurant and theater to show the Cousteau underwater films and the Calypso replica would also be included.

As for the French, what do they think of Norfolk's proposed relationship with their native son? "It's a good idea. I see nothing wrong with a Frenchman going to organize a scientific center abroad," said a spokesman for the French Embassy in Washington.