We investigate theoretically the electronic structure of regular and statistical copolymer chains containing segments of poly(p-phenylene vinylene) (PPV) and its dimethoxy-substituted derivative, poly(2,5-dimethoxy-1,4-phenylene vinylene) (DMeOPPV). Such copolymers have recently been shown to present remarkable electroluminescence properties. The calculations on the copolymer chains are performed on the basis of the negative factor counting technique coupled to the valence effective Hamiltonian method. The eigenfunctions of the upper occupied and lower unoccupied levels are calculated explicitly using the inverse iteration technique, and the degree of localization is determined via the inverse participation number approach. It is shown that the electronic structure of PPV/DMeOPPV copolymers is strongly affected by both the concentrations and relative locations of the parent polymer moieties along the chains. The appearance of clusters of dimethoxy-substituted units leads to energy gaps that are smaller than those of the parent polymers and to a spatial localization of the upper occupied levels within the DMeOPPV clusters, while the lower unoccupied levels remain smoothly delocalized over the unsubstituted regions. Our results thus indicate that electron-hole recombination processes should take place preferentially at the interfaces between PPV and DMeOPPV segments. The evolution of the PPV/DMeOPPV copolymer band gaps as a function of the concentration in dimethoxy substituted rings is compared to experimental photoluminescence and absorption data.