In a letter to the national committee, the 16 delegates -- all supporters of Texas Rep. Ron Paul -- said the Massachusetts Republican Party "changed the rules" when it disqualified them, the Boston Globe reported Monday.
The delegates were elected in April caucuses when they defeated many of Romney's chosen delegates.
The filing starts a formal process for the would-be delegates, who hope to convince national GOP officials they were unfairly disqualified from the Republican National Convention Aug. 27-30 in Tampa, Fla.
An RNC committee is expected to consider the challenge by mid-August, the Globe said, but a decision isn't expected until the week before the convention. Any appeal could be considered by the convention's credentials committee when the event begins.
Supporters of Paul, who has stopped campaigning for his party's nomination, said they still hope for a large presence at the convention.
In their letter, the "Liberty" delegates say they were properly elected in April, but disqualified after they didn't provide timely affidavits pledging their support to Romney. They argue that the affidavits were not included in state or federal rules and that they got them "less than one week before an arbitrary deadline" to return them notarized, the Globe said. While some met the deadline, others missed it and some filed an affidavit in which they promised to follow the state's rules, not pledging to support Romney by name.
The state GOP determined it had just cause to disqualify the delegates, replacing them with 16 others, the challenge said.
One national Republican leader knowledgeable of the situation told the Globe he thinks the Paul supporters don't intend to support Romney, but cause trouble at the convention.
"If they're not willing to say that, that's their prerogative," the official said. "But clearly they're not Mitt Romney delegates."
"It's a really awkward situation. A lot of them are trying to get guest passes with the other Liberty delegates," Brad Wyatt, one of the disqualified delegates, told the Globe. "We're cautiously optimistic that we'll get some good decisions."