Pasty anhydrous composition possibly containing up to 1% by weight of water, for simultaneously bleaching and dyeing human keratin fibres, and in particular the hair, and comprising, in a medium that is suitable for dyeing:- at least one peroxygenated salt,- at least one alkaline agent,- 15% to 35% by weight, relative to the total weight of the composition, of at least one inert organic liquid ...