A product for oxidatively coloring and/or lightening keratinic fibers includes (1) a dispenser, which has two chambers (A) and (B) separate from one another; an outlet opening (C) communicating with chamber (A) and with chamber (B); (2) a preparation (a) in chamber (A), which preparation includes one or more thickening polymers in a total amount by weight (G1) of 0.1 to 20%, based on preparation (a); one or more fatty components in a total amount by weight (G2) of 0.1 to 20%, based on preparation (a); and (3) a preparation (b) in chamber (B), which preparation includes one or more thickening polymers in a total amount by weight (G3) of 0.1 to 20%, based on preparation (b), and one or more fatty components in a total amount by weight (G4) of 0.1 to 20%, based on the total weight of the preparation (b). The weight ratio of G1/G3 has a value of 0.5 to 2.0 and the weight ratio of G2/G4 has a value of 0.5 to 2.0.