Abstract: Process for dyeing, by exhaustion, textile fibres of basic character with anionic dyestuffs in a solvent medium in the presence or absence of water wherein the dyebath is a homogeneous ionising liquid medium and the cations of the bath are replaced by H.sup.+ protons in the course of the dyeing, the latter being effected at a temperature equal to or less than 80.degree.C. and apparatus for use of this process which comprises apparatus for dyeing according to the process claimed in claim 1 which comprises a dyeing vessel for dyeing with solvents, a circuit for removing the dyebath continuously or by fractions, means for substituting the cations of the bath with H.sup.+ protons, a recycling circuit ensuring the reintroduction into the vessel of the bath from which all or part of its cations have been removed, means for regulating the flow and means for regulating the temperature.