In a process for preparing copolymers of ethylene with C.sub.3 -C.sub.10 -alk-1-enes, the polymerization is carried out at pressures in the range from 1000 to 3500 bar and at from 200 to 280.degree. C. in the presence of a catalyst system comprising as active constituents a donor-substituted monocyclopentadienylamido(transition metal) complex compound of the following formula, a compound capable of forming metallocenium ions and, optionally, a trialkylaluminum compound; ##STR1## wherein y is ##STR2##