The present invention relates to a process for relaxing curls and/or straightening keratin fibres, such as the hair, which comprises the application to the fibres of one or more compositions comprising reducing agents, and a step of heat treatment of the fibres by means of a heating tool. A subject of the invention is also the use of the composition(s) comprising reducing agents in a process for relaxing curls and/or straightening keratin fibres. Finally, a subject of the invention is a multi-compartment device or “kit” suitable for carrying out such a process.