Cosmetic compositions comprising at least one structuring polymer chosen from polymers of following formula (I): ##STR00001## in which n denotes a number of amide units, such that the number of ester groups represents from 10% to 50% of the total number of ester and amide groups; R.sup.1 is, in each case, independently an alkyl or alkenyl group having at least 4 carbon atoms; R.sup.2 independently represents, in each case, a C.sub.4 to C.sub.42 hydrocarbonaceous group, provided that 50% of the R.sup.2 groups represent a C.sub.30 to C.sub.42 hydrocarbonaceous group; R.sup.3 independently represents, in each case, an organic group provided with at least 2 carbon atoms, with hydrogen atoms and optionally with one or more oxygen or nitrogen atoms; and R.sup.4 independently represents, in each case, a hydrogen atom, a C.sub.1 to C.sub.10 alkyl group or a direct bond to R.sup.3 or another R.sup.4, so that the nitrogen atom to which both R.sup.3 and R.sup.4 are bonded forms part of a heterocyclic structure defined by R.sup.4--N--R.sup.3, with at least 50% of the R.sup.4 groups representing a hydrogen atom and at least one solid substance that has a melting point of 45.degree. C. or greater.