A process for dyeing and/or bleaching keratin fibers, comprising applying to the fibers, which can be wet or dry fibers,
- composition (A) comprising at least one basifying agent, and
- anhydrous composition (B) comprising hydrogen peroxide and/or at least one hydrogen peroxide precursor,
- successively and without intermediate rinsing,
- wherein composition (A) and/or composition (B) comprise at least one fatty substance not containing any carboxylic acid functional groups, such that the total amount of the at least one fatty substance not containing any carboxylic acid functional groups after mixing composition (A) and composition (B) is greater than 20% by weight.