A process for preparing ethylene homopolymers and copolymers in a tubular
reactor having two or more polymerization zones at temperatures of
between 150.degree. C. and 350.degree. C. and pressures in the range from
500 to 5000 bar, using oxygen as initiator, which comprises using, as
molar mass regulator, one or more aliphatic ketones of the formula I,
##STR00001## where the variable R.sup.1 is a C.sub.1-C.sub.6-alkyl or
C.sub.3-C.sub.12-cycloalkyl, ethylene homopolymers and copolymers
obtainable therefrom and their user for producing injection-molded
products in the cosmetics, medical and food sectors are described.