Multifilamentary Nb3Sn-based superconducting composites manufactured by an internal-tin method have been studied by transmission (TEM) and scanning (SEM) electron microscopy. The main goal of this study is to reveal the effect of diffusion annealing regimes as well as the external diameter of the wires on the structure of nanocrystalline Nb3Sn layers (average grain size, grain size distribution, layer thickness, amount of Sn, etc.). It is demonstrated that multistep diffusion annealing results in quite a complete transformation of Nb filaments into Nb3Sn though some amount of the residual Nb remains in the filaments center. With an external diameter decrease the superconducting layers structure has been found to refine and get somewhat more uniform. An additional high-temperature annealing results in marked growth of Nb3Sn grain sizes and their scattering in sizes, which may negatively affect the current-carrying capacity of a wire.