Abstract: An ethylene-polymer-based composition obtained by mixing, in the melt: 100 parts by weight of an ethylene polymer withfrom 0.0005 to 0.1 part by weight of a compound (a) with the ability to generate free radicals andfrom 0.0005 to 0.1 part by weight of coagent (b) chosen from among the C.sub.3 to C.sub.12 alkenes and the C.sub.5 to C.sub.16 alkadienes.This composition has clearly improved melt strength. It is very suitable for extrusion and rotational molding and in particular for the extrusion of tubes intended for conveying fluids under pressure. The invention also relates to a process for obtaining the composition and using it for the manufacture of shaped articles, and to shaped articles.