Sen. Edward M. Kennedy (D-Mass.) may have an inheritance problem now that his candidacy for the Democratic presidential nomination is all but official.

The formation of an "exploratory" campaign committee, sanctioned by Kennedy, is expected next week. As a result, the draft-Kennedy groups around the country are suddenly wondering what to do about the money they've raised. They can't give much of it to Kennedy without running into all sorts of difficulties under federal election laws.

President Carter's reelection committee, meanwhile, is thinking of asking that the money these groups have already spent be counted as though the expenditures had come out of Kennedy's pockets.

It is still tentative, but Tim Smith, counsel for the Carter-Mondale committee, said it is considering filing a new complaint with the Federal Election Commission along those lines, especially concerning spending in the key early states of Iowa, New Hampshire and Florida.

"It is a very serious matter politically," Smith said yesterday. "Legally, the question is whether these are independent expenditures. If they are not, they should count against the limits."

In New hampshire, for instance, the limit for spending on the Feb. 26 Democratic primary there is $264,000. Dudley Dudley, head of the draft-Kennedy group there says her organization, New Hampshire Democrats for Change, has raised about $65,000 and has spent about half in its effort to get the senator into the race.

They'd also been planning to raise $20,000 more at fund raisers Nov. 5 here in Washington and Nov. 8 in Columbus, Ohio, but these have now been canceled, just as the invitations were about to go out in the mail.

Dudley said two other fund-raisers next weekend, in Washington and in Lexington, Mass., will go ahead on schedule, but it is far from clear what will be done with the proceeds.

"My guess is that, if they're smart, they will dump that money somehow --buy Kennedy buttons and give them away--and then go out of business," said one source familiar with the FEC's complicated rules. This source, and others, pointed out that the 60 draft-Kennedy Committees around the country could give only $1,000 each to Kennedy's official committee.

In Iowa, according to Matthew Wanning, head of the draft-Kennedy organization there, a $1,000 donation is about all they could afford anyway. He said his committee has raised about $32,000 and has spent about $30,000 so far. "We're going to need some of the money just to close up shop," he added.

In any case, the draft-Kennedy leaders say they have not been seeking, nor getting, advice from Kennedy's inner circle, lest they compromise their Independent status. The FEC has ruled that the draft-Kennedy groups are independent, and thus can raise up to $5,000 each from individuals instead of observing the $1,000 limit on contributions to single-candidte committees such as the president's.

The Carter-Mondale Committee has already filed one complaint with the FEC, alleging that the various draft-Kennedy groups were really part of a coordinated effort and should be bound by the same limits applicable to the Carter campaign.

"To make it absolutely clear that they're acting independently, it may be best if they terminate," acknowledged one prospective official of Kennedy's "exploratory" committee.

A Carter campaign official said the president's committee might still approach the Kennedy camp to suggest a voluntary agreement providing that:

Draft-Kennedy money raised and spent in Iowa, New Hampshire and, Florida would count against his spending limits in those states.

Surplus draft-Kennedy money would be put in an escrow account at, the Democratic National Committee, to be used in the general election by whoever wins the Democratic nomination.

The Carter campaign seems to have little expectation of winning Kennedy's consent, however. About all they can offer in return, one of the president's strategists said, is a promise not to file another complaint with the FEC.