The present invention relates to a composition suitable for treating hair comprising a polymer selected from the group consisting of a branched polylysine and a branched polylysine in which to 80% of the amino groups present in the branched polylysine are derivatized so that they bear one or two substituents, and comprising at least one surfactant. Furthermore, the present invention relates to a branched polylysine in which 1 to 80% of the amino groups present in the branched polylysine are derivatized so that they bear one or two substituents, wherein these substituents are acyl groups having 6 to 24 C-atoms. Furthermore, the present invention relates to the use of a branched polylysine or of the branched polylysine in which amino groups are derivatized or of the said composition for treating hair. Furthermore, the present invention relates to a process for treating hair comprising contacting the hair with a branched polylysine or with the branched polylysine in which amino groups are derivatized or with the said composition.