The present disclosure relates to an agent for dyeing and/or bleaching keratin fibers, comprising: composition (A) comprising at least one basifying agent, and anhydrous composition (B) comprising hydrogen peroxide and/or at least one hydrogen peroxide precursor, 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 is present in the mixture of composition (A) and composition (B) in an amount greater than 20% by weight. The disclosure also relates to a process for treating human keratin fibers using this dyeing and/or bleaching agent, and a multi-compartment kit comprising this dyeing and/or bleaching agent in at least two parts.