Mr Trimble said: "To those who have been engaged on all sides in paramilitarism - the time has come for them to let go, to let us go into the future."
He said there would not be peace and democracy until the private armies were gone.
Mr Trimble said he was not prepared to compromise with the integrity of the Good Friday Agreement. "We are not going to produce a state or a society which is corrupted and tainted by paramilitarism."
One of the fundamental elements of the agreement, he said, was that it offered those who had been involved in paramilitarism "the opportunity to come in from the cold and to be involved in normal democratic practise".
Mr Trimble took time out from negotiations in Stormont to address the sixth-form political societies of four Catholic and Protestant schools in Downpatrick, County Down.
He told them: "We are not going to have peace and democracy if there are private armies in existence in Northern Ireland. A private army, even inactive but still in being, distorts the way society operates."
Without naming the IRA, Mr Trimble made it clear he was not singling them out.
"Nobody is innocent in this respect," he said.Reuse content