Poly-N-acylalkyleneimines corresponding to the following formula ##STR1## are used as an oxidatively crosslinking constituent in paints. In formula (I), R--CO represents the acyl radical of a mono- or polyunsaturated, aliphatic C.sub.16-22 carboxylic acid or a mixture of such radicals, R'--CO represents the acyl radical of a C.sub.1-22 carboxylic acid or a mixture of such radicals and x and y represent the percentages by weight of the particular polymer units, x assuming values of 20 to 100% and preferably 20 to 95% and y assuming values of 80 to 0% and preferably 80 to 5%. The indices m and n independently of one another may assume the value 2 or 3.