The vote count begins today on a membership referendum designed to resolve a bitter power struggle inside the maritime union that provides shipboard engineers to U.S. steamship lines.

The final tally will not be known until Sunday evening.But like so many other events in the recent history of the Marine Engineers Beneficial Association, the referendum - which asks members to reaffirm the 1988 merger of MEBA's District No. 1 and the National Maritime Union - is mired in controversy and almost certain to be challenged in court. (See related story, Page 3A.)

Opponents of the merger say the referendum vote will be meaningless because most shipboard engineers already have left the NMU.

"This bogus referendum, under a cloud, shouldn't have any significance whatsoever," said Gordon M. Ward, president of District No. 1-Pacific Coast District of MEBA. Members of that group recently voted to abolish the merger and to revert back to their original status as PCD.

The Ward group organized its own referendum on the merger that "will be the true gauge of the licensed officers' feelings," said Mr. Ward.

But the leaders of MEBA/NMU said the vote results will show they are supported by the membership of the union and convince the AFL-CIO, other maritime unions and the shipping industry to recognize their group as the legitimate representative of the engineers.

"In my mind, after this merger reaffirmation, (the Ward group) will be a non-AFL-CIO entity, a scab outfit, and will not be able to utilize the name MEBA or PCD" for Pacific Coast District, said Alexander C. Cullison, president of District No. 1/MEBA-NMU.

A possible court challenge is bad news for the maritime industry, which is looking to the referendum to settle which union faction they should go to for their engineers.

"There very well could be litigation, and that concerns us," said Martin Oppenheimer, the attorney for two shipping employer groups that hold collective bargaining contracts with the MEBA. "We think the parties should concentrate on the growth of the industry rather than internal union problems."

There are indications that the dispute may be settled by the AFL-CIO.

On Wednesday, Lane Kirkland, AFL-CIO president, met with Mr. Ward to discuss the situation, union sources said. Earlier this month, he met with Mr. Cullison.

The vote emerged from a stipulation agreement between attorneys for MEBA/ NMU; Arthur Fox, the attorney for Albert Jackson, an NMU seaman from Delaware who filed a lawsuit against the merger, and U.S. Federal Judge Thomas P. Greisa.

That merger was tarnished, both sides in the dispute agree, because C.E. ''Gene" DeFries, then-union president, and other officers did not reveal key aspects of their agreement to the membership.

These included the secret disbursal to Mr. DeFries and four other MEBA officials of $2 million in severance payments, and proposals - never carried out - to combine the assets of the NMU and MEBA pension plans.

Those actions sparked a rebellion within the union that climaxed last month with the sudden resignation of Mr. DeFries.

Two weeks later, the Ward group joined with a separate engineers district of the union and declared themselves the one, true National MEBA.

The other National MEBA group, which includes the NMU and several union districts that represent workers outside of the maritime union, is headed by Mr. Cullison.

In addition to the merger issue, the MEBA/NMU referendum asks members to affirm six changes in the union constitution approved by a special convention of District No. 1 in January.

The Ward group refused to participate in the agreement between Mr. Jackson's attorney and MEBA/NMU because it did not include procedural safeguards.

They also objected to the 57-day period allotted for the vote, which they said made it difficult for seagoing members of either MEBA or NMU to participate.

Other factors were the MEBA/NMU's insistence on including the votes of shoreside units and the union's refusal to state whether the merger would be dissolved if only one of the two parties, the engineers or the NMU, should vote no.

"They're allowing people to vote who had nothing to do with the merger," said Mr. Ward. "It's a sham."

But the Ward group has encouraged its members to vote in the referendum to ''send a message" to the leaders of MEBA/NMU, he said.

Mr. Cullison said he is confident that the majority of District No. 1 favors the merger with NMU.

But asked what he would do if the union determined that a majority of the engineers group was opposed, he replied: "I'll have to give you a whole bunch of new statements. I haven't even thought of what to say."

After the merger is "reaffirmed," Mr. Cullison said, he would move swiftly to "put this union back together" and restore property, including union halls, owned by MEBA/NMU.

The AFL-CIO may resolve the situation by granting the MEBA charter to the Ward group and the NMU charter to the Cullison group.

Under one scenario, the Cullison group, which would include the two shoreside districts of MEBA/NMU, would be given another title while Ward's group and District No. 2 would be recognized as National MEBA.