The present invention relates to a composition for treating keratin fibers, and in particular human keratin fibers such as the hair, comprising, in a cosmetically acceptable medium, one or more alkanolamines, one or more basic amino acids and one or more additional alkaline agents chosen from aqueous ammonia; ammonium salts of acids whose pKa at 25° C. is greater than 4; alkali metal or alkaline-earth metal hydroxides, carbonates, carbamates and hydrogen carbonates. The present invention also relates to processes for bleaching and/or dyeing keratin fibers, and also to multi-compartment devices or ‘kits’ for performing these processes.