The present application relates to a process for the manufacture of copolymers of ethylene and of at least one vinyl ester, comprising the following steps: a) fermentation of renewable starting materials so as to produce at least one alcohol comprising ethanol; b) dehydration of the alcohol obtained so as to produce at least one alkene comprising ethylene and, optionally, purification of the alkene so as to obtain ethylene, c) copolymerization of the ethylene with at least one vinyl ester, d) isolation of the copolymer obtained. The application also relates to the copolymers of ethylene and of at least one vinyl ester in which the ethylene is at least partly obtained from renewable starting materials, and to uses thereof.