A third man is in a serious condition in hospital
following the incident late on Saturday
Two servicemen have died during a training exercise in hot conditions in the Brecon Beacons in Powys.
A third man is in a serious condition in hospital following the incident late on Saturday afternoon.
An investigation is taking place but it is understood live ammunition was not involved.
It is believed investigations will focus on the weather conditions and the nature of the training exercise.
The deaths occurred on the hottest day of the year so far in Wales with temperatures reaching 30C (86F) in Powys.
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"
Next of kin have been informed, said the Ministry of Defence (MoD).
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' 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.
Defence Editor for the Evening Standard Robert Fox:
"We have to be very careful when the temperatures
are shooting up"
"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," he said.
"It's one of the most challenging terrains."
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.
"It probably would've been cooler on the Brecon Beacons yesterday than it is in the desert of Afghanistan," he said.