The influence of the composition and thermal history on the type of lattice developed has been studied by wide-angle X-ray diffraction measurements in three vinyl alcohol-ethylene, VAE, copolymers with different compositions, which were crystallized from the melt at various cooling rates. The results are compared with those of the corresponding homopolymers, poly(vinyl alcohol) and low-density polyethylene. Both the composition and the cooling rate have been found to determine the crystalline structure of these VAE copolymers. Thus, for the samples slowly crystallized from the melt, a monoclinic lattice is obtained for copolymers VAE71 and VAE68 (with compositions of 71 and 68 mol % VA, respectively) while an orthorhombic lattice has been found for copolymer VAE56 (56 mol % VA). The effect of the cooling rate is very important, since copolymers VAE71 and VAE68 lead to the orthorhombic form when the samples are quenched from the melt. Copolymer VAE56 has been found to crystallize in an orthorhombic lattice under all the crystallization conditions here studied. The polymorphism exhibited by these copolymers is not the usual case for two different unit cells with well-defined lattice parameters : VAE71 and VAE68 show, by the influence of the cooling rate, a continuous change of some of the lattice constants. For instance, the angle beta of the monoclinic lattice decreases smoothly from an "equilibrium" value of about 92.2 degrees in the slowly crystallized samples to a final value in the quenched samples of 90 degrees (orthorhombic unit cell). The degree of crystallinity determined from the X-ray diffraction patterns has been found to be in the quenched specimens considerably smaller than that in the slowly crystallized samples, standing in contrast to the constancy of the enthalpy of melting. Moreover, it seems that there are no differences in the melting temperatures between the two crystalline modifications.