The present invention concerns cosmetic compositions for coloring hair comprising at least one direct hair dye and a carrier system for the at least one direct hair dye, the use of such compositions in cosmetic formulations for coloring hair and processes for the production of the compositions. To provide a possible way with which the permanence of the bond of direct hair dyes to the hair can be improved, with the aim of direct dyes remaining on the hair for as long as possible to deliver the desired hair color in the desired quality for as long as possible, according to the invention there are proposed compositions of the aforementioned kind in which the carrier system includes lipid vesicles having one or more lipid membranes, wherein the at least one direct hair dye is contained in the lipid vesicles and the lipid vesicles have a positive surface charge, wherein the positive surface charge is caused by the lipid vesicles in the lipid membrane or membranes in addition to the lipids from which the vesicles are made up having positively charged alkyl trimonium salts as charge generators.