Ethylene-(vinyl acetate) (EVA) copolymers, obtained by emulsion copolymerization at low and medium pressure (1-~ MPa), have been examined for composition, compositional heterogeneity, character of branching and distribution of comonomer units along the polymer chains. The copolymers were characterized in respect of compositional and configurational heterogeneity. The analysis of the triad populations suggests the existence of two parts in the polymer chains. The comonomer units in one part show a tendency to alternate, while the ethylene units in the other part show enhanced tendency to form blocks. Investigation of branching of EVA emulsion copolymers performed by methods insensitive to the state of the macromolecules in solution (tH-and ~3C-NMR) showed that long-chain and short-chain alkyl branches were present in copolymers irrespective of composition and molecular weight. The long-chain alkyl branching is less than in the bulk copolymer obtained at high temperature and high pressure. The microstructure of EVA emulsion copolymers should be taken into account when interpreting results on solution properties of macromolecules as well as their behaviour in the solid state and in the melt.