Thermal characteristics of ethylene-vinylacetate (EVA) copolymers having vinylacetate contents ranging from 5 to 40 w/w % are studied by differential scanning calorimetry. It is first shown that EVA copolymers having a vinylacetate content lower than 30 w/w % obey the Flory and Burfield theories of copolymer crystallisation. The minimum sequence length of CH2 ethylenic entities required to participate in a crystalline lamella is also deduced. One can conclude that EVA copolymers represent cases of "total exclusion" of the noncrystallizable comonomer. Moreover, it is observed that when the vinylacetate content is increased, the relative quantity of polyethylene amorphous phase increases and the degree of crystallinity decreases; whereas the beta transition temperature of a characteristic-oriented amorphous phase is kept constant. A phase model of ethylene-vinylacetate copolymers, based on an enrichment process of the interlamellar amorphous phase by polyethylene segments originating from the crystalline phase, at increasing vinylacetate content, is proposed.