We have observed a periodic superlattice modulation in Nd2CuO4 and in the "electron-doped" Nd2CuO4-xFx and Nd2-xCex-CuO4 by electron diffraction and microscopy. The superlattice modulation characterized by a wave vector q=( 1 4 1 4,0) parallel to the Cu-O plane was found in both superconducting and non-superconducting samples, but most of the samples examined were not homogeneous with respect to the superlattice. The orthorhombic superlattice phase is found to exist in four possible variants with its c-axis parallel to the four equivalent  zone-axes in the underlying tetragonal lattice. Samples quenched from high temperature invariably showed no superlattice or superconductivity; bulk superconductivity and regions of superlattice were observed on annealing in the range 250-750°C. We believe that oxygen migration is responsible for this disproportionation into superlattice and nonsuperlattice regions.