Dead soldiers in Powys served with Territorial Army
Two solders who died during a training exercise in the Brecon Beacons in Powys were serving with the Territorial Army, the BBC understands.
A third soldier is in a serious condition after Saturday afternoon's incident, which is thought to have been linked to the hot weather.
The Ministry of Defence has refused to comment on reports they were taking part in an SAS selection process.
It is understood live ammunition was not involved.
The Brecon Beacons is home to the Infantry Battle School and makes up one of the largest military training areas in Britain.
The MoD has released little information about the two soldiers who died, but BBC News understands they were with the TA.
An investigation into their deaths will focus on the weather conditions and the nature of the exercise the were involved in.
The deaths occurred on the hottest day of the year so far in Wales, with temperatures reaching 30C (86F) in Powys.
The MoD said in a statement: "The MoD can confirm that it is working with Dyfed-Powys Police to investigate an incident during a training exercise on the Brecon Beacons on Saturday in which two members of military personnel died.
"The two servicemen's next of kin have been informed. More information will be released in due course but it would be inappropriate to comment further at this stage."
The Brecon Beacons forms one of Wales's national parks and is used for military training because of its relative remoteness.
The infantry regiments of the British army train at Sennybridge in the area and there is an Army base in Brecon.
Mayor of Brecon and Powys county councillor Matthew Dorrance said: "It's incredibly sad for the friends and family of the people who have lost their lives and thoughts are with the person who is injured.
"In one way we've been blessed with the weather but for people working in this heat, they're tough conditions."
Mr Dorrance said local people regularly saw troops training in the area and military vehicles parked on the side of the road.
"We're proud of our links with the military in the town," he said.
Maj Alan Davies, who was involved in contingency planning during the first Gulf War, said the Beacons were used by "all sorts of people for all sorts of things".
"On one end of the spectrum you have cadets being taken for mountain walking and at the other end of the spectrum the SAS use it. It's one of the most challenging terrains," he said.
Maj Davies said the men may have been carrying very heavy equipment and working to a deadline, which meant they would have been pushing themselves very hard.