Progress towards resolving the decommissioning issue could be made by allowing Gen John de Chastelain to begin a "stocktaking exercise" of paramilitary arsenals, according to an SDLP Assembly member's position paper.
Although issued in the name of Mr Joe Byrne, who represents West Tyrone, it is likely to also reflect the thinking of senior party members.
Mr Byrne argues that the "political reality is that immediate decommissioning is not an `up front' requirement of the agreement, but rather it is a core requirement which should be concluded over a two-year period."
The Ulster Unionist Party and Sinn Fein "must accept their political responsibilities", the UUP by agreeing to the creation of a shadow executive of ministers, ein must also accept their political responsibilities, and deliver and Sinn Fein by delivering a signal from the republican movement of its intent and desire to co-operate with the arms decommissioning body.
"A verifiable stocktaking exercise" by Gen de Chastelain of paramilitary weaponry would allow him to ascertain the true intentions and commitment of republicans and loyalists, Mr Byrne says. Decommissioning "must be an evolutionary process, directly contingent and dependent upon the new political structures being put into motion and becoming fully operational".
In a statement the Sinn Fein chief negotiator, Mr Martin McGuinness, said the two governments could not ein or any other party to the Agreement. Nor can the two governments allow the First Minister and Ulster Unionist leader, Mr David Trimble, "to stall the full implementation of the agreement in order to placate the rejectionists in his party any longer".
The recently-established group, Families Acting for Innocent Relatives (FAIR), said in a statement it had become gravely concerned that a "fudge" was about to emerge on decommissioning.
"We need real and full decommissioning as a starting block towards real and lasting peace, and only then will the real fear we suffer begin to be removed. We want to bring up our children to love their neighbours, not fear them," the group said.
The British-based cross-party peace group, New Dialogue, has proposed in a letter to Gen de Chastelain that the decommissioning body "should classify the weapons now illegally held by paramilitaries by reference to their destructive power. It should draw up a schedule, with dates, for decommissioning of all illegally-held weapons, starting with the most destructive."