The twin microstructure of superconducting La2CuO4+delta crystals with delta ranging from 0.02 to 0.04 has been studied by neutron and X-ray scanning of the reciprocal space and high-resolution neutron diffraction. The crystals studied were of two types with respect to the low-temperature diffusion of excessive (nonstoichiometric) oxygen: those with and those without macroscopic phase separation. It is shown that for both types of crystals, twinning is accompanied by the formation of almost equivalent systems of domains (transformational twins). The configurations of these domains provide the formation of mainly coherent interdomain boundaries. In the La2CuO4+delta crystals studied, which undergo the macroscopic phase stratification during cooling, the volume of the transient regions with the distorted structure is rather small, which seems to be a factor promoting diffusion of excessive oxygen.