The two soldiers who died on the Brecon Beacons on Saturday were taking part in a selection process for the SAS reserves, sources have told the Press Association.
According to the SAS website, the elite force has two reserve units which recruit male personnel from both military and civilian backgrounds.
The website states that they are "tasked to the highest level" and must complete a two-phase selection process demanding about 80 days over 12 months.
The initial 'Aptitude' test is described as "a progressively arduous phase, requiring greater expenditure of physical energy, designed to select volunteers with the right qualities".
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.