On Saturday, the UVF and the UDA said they had both engaged in "historic acts" of decommissioning.
The leadership of the UVF/RHC said its disarmament process was overseen by the Independent International Commission on Decommissioning (IICD) and in front of international witnesses.
It said the process had begun last Autumn but had been "suspended" following the dissident republican killings of a policeman and two soldiers in March.
The process resumed after government assurances were given "that those responsible would be vigorously pursued".
Dawn Purvis: 'It is time to move on'
The leader of the UVF-linked Progressive Unionist Party, Dawn Purvis, said the "war is over", adding Saturday was a "momentous day".
She said it showed that "peaceful, stable, inclusive democracy" was the way forward.
She added: "Eventually loyalists and republicans must sit down for the good of our country, if we claim to be patriots."
PUP representative Billy Hutchinson, who was a UVF prisoner, said the move "cements the peace process".
In a separate statement, the UDA confirmed it had started a process that would lead to the destruction of all its arms.
It said an act of decommissioning had been overseen by General John De Chastelain's decommissioning body.
It said: "There is no place for guns and violence in the new society we are building. It is time to work for a better future."
Frankie Gallagher, from the Ulster Political Research Group (UPRG), which has links with the UDA, denied they were negotiating a pay-off to complete decommissioning.
"This is a process that we believe has to be done for the right reasons," he said.
The decommissioning body later confirmed that it had witnessed a decommissioning event involving arms belonging to the UDA and the Ulster Freedom Fighters.
"This is a significant move and we look forward to completing the process of putting all UDA/UFF arms beyond use at an early opportunity," a spokesperson said.
The latest decommissioning comes ahead of Mr Woodward's August deadline for significant progress on loyalist arms.
Speaking on Saturday, Mr Woodward said: "I have always kept faith with the peace and political process of which the decommissioning legislation has played a crucial part."
The decommissioning moves by the loyalist paramilitary groups were broadly welcomed by the majority of Northern Ireland's political parties.
First Minister Peter Robinson said:"I fully welcome this decision by each of the loyalist groups. I believe they have taken the right step, both for their own communities and for Northern Ireland as a whole. "
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