The men, named only as 1A and 1B, both denied a single charge of "negligently performing a duty" by failing to take reasonable care for the health and safety of the candidates taking part in the exercise in July 2013.
1A is a serving captain who was the training officer in charge of the march, and 1B, a former warrant officer, was the chief instructor on the exercise.
Lance Corporal Edward Maher and Lance Corporal Craig Roberts were pronounced dead on the Brecon Beacons after suffering heatstroke.
Corporal James Dunsby died at Birmingham's Queen Elizabeth Hospital from multiple organ failure more than two weeks later.
In a hearing lasting less than half an hour at Colchester Military Court, 1A and 1B appeared behind a screen and entered not guilty pleas.
Their identities, which are protected by an anonymity order, were given to Judge Advocate General Jeff Blackett, along with their ranks and numbers.
A panel of five military personnel will adjudicate the three-week trial beginning on 3 September.
The pair could face up to two years in prison and dismissal if convicted.