A judge entered not guilty verdicts against Padraic Wilson, Briege Wright, Seamus Finucane,  and Agnes McCrory.
The charges allegedly concerned several meetings held by the IRA in the late 1990s and 2000.
All four had denied the charges at arraignment.
Mr Wilson, 53, of Hamill Park, Andersonstown, Belfast, was the only one of the four present in the public gallery at Belfast Crown Court to hear the verdicts.
He was due to go on trial at a non-jury court accused of two counts of "arranging or assisting a meeting of three or more people, knowing that the meeting was to support a proscribed organisation, namely the Provisional Irish Republican Army''.
Agnes McCrory, 63, of Dermot Hill Road, Seamus Finucane, 57, of Hawthorn Hill, Hannahstown, and Briege Wright, 56, of Glasmullin Gardens, all west Belfast, were accused of professing to be members of the Provisional IRA, making threats, and organising or addressing meetings of PIRA.
The case had been listed for mention only on Thursday.
However, a prosecuting lawyer asked the judge that the charges "be left on the books and not to be proceeded without the leave of the Crown Court of the Court of Appeal''.
But a defence counsel said in the case last month of his client Martin Edward Morris, 49, of Welbeck Road, London, the prosecution offered no evidence against him on a charge of membership of the Provisional IRA.
"In the light of that decision, we say that the prosecution in this case should offer no evidence in the same terms," he said.
The prosecution lawyer told the court the prosecution was now "not offering evidence'' evidence against the four accused.
She added that the prosecution was also not "offering any evidence'' against Mr Morris who was awaiting trial on separate charges.
The Belfast Recorder said that as a result of the prosecution decision, he would enter "not guilty verdicts'' on all 13 charges faced by Morris.
Four people due to stand trial charged with arranging Provisional IRA meetings have had the charges dropped after the prosecution offered "no evidence'' against them.