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