The Ministry of Defence has named one of the soldiers who died on a training exercise in the Brecon Beacons in Wales as Lance Corporal Craig Roberts.
The other was identified only as "another Army reserve soldier".
The soldiers' families have been informed.
Emotional tributes have been paid to a third army reserve soldier who died from injuries sustained during SAS selection training.
One of two Army reservists killed in a military exercise in the Brecon Beacons on Saturday has been named as Lance Corporal Craig Roberts.