The pair work for Staffordshire fire and rescue service.
Two firefighters have been injured on a training exercise near Buxton.
The incident involving members of the Staffordshire fire service happened on Sunday while carrying out rope training.
One of the victims is still receiving treatment for life-changing injuries.
Chief Fire Officer, Becci Bryant, said: “Everyone across Staffordshire Fire and Rescue Service is shocked and saddened by this incident and our thoughts remain with our injured colleagues and their families and friends at this difficult time and we would ask that their privacy is respected. We are working to support them and other colleagues who have been affected by this.”
The HSE has been informed and Derbyshire Fire & Rescue Service will undertake an independent investigation into the circumstances around this incident.