A process for the preparation of ethylene homopolymers and ethylene copolymers with minor amounts of C.sub.3 -C.sub.6 -.alpha.-monoolefins by polymerizing the monomer or monomers at from 30.degree. to 200.degree. C. under a pressure of from 0.1 to 200 bars, by means of a supported catalyst (1) which contains a chromium-hydrocarbon complex (1.2) on an inorganic oxide carrier (1.1), wherein
- (1) a supported catalyst is employed, which contains (1.1) on a finely divided, porous, inorganic oxide carrier, having a particle diameter of from 1 to 1,000 .mu.m, a pore volume of from 0.3 to 3 cm.sup.3 /g and a surface area of from 100 to 1,000 m.sup.2 /g and which has the formula SiO.sub.2.aAl.sub.2 O.sub.3, where a is a number from 0 to 2, (1.2) a chromium-hydrocarbon complex of the formula
- RCrACrR
- where R is a cyclic and/or open-chain hydrocarbon or hydrocarbon radical which contains 2n and 2n+1 carbon atoms respectively and from 1 to n non-cumulated double bonds, n being an integer from 2 to 10, Cr is chromium and A is cyclooctatetraene or a divalent n-octatetraene radical, which is unsubstituted or in which up to 8 hydrogen atoms of the cyclooctatetraene or n-octatetraene radical can be substituted by C.sub.1 -C.sub.4 -alkyl,
- (2) with or without a co-catalyst of the formula ##STR2## where X is chlorine, hydrogen, R' or OR', Y is R' and OR' and R' is C.sub.1 -C.sub.18 -alkyl, with the provisos that (i) the supported catalyst (1) contains from 0.01 to 10% by weight, calculated as chromium and based on carrier (1.1), of the complex compound (1.2) and (ii) that, where the co-catalyst is present, the atomic ratio of chromium in the supported catalyst (1) to aluminum in the co-catalyst (2) is up to 1:1,000.