Evidence of structural inhomogeneities in two high-transition-temperature superconductors, YBa2CU3O7-delta and Nd2-xCexCuO4-y, is presented. When samples were illuminated by highly collimated x-rays produced on a synchrotron wiggler, small changes in the lattice were detected over a spatial scale of 10 micrometers. These changes are interpreted as evidence of variations in the oxygen content in one case and in the cerium content in the other; both affect the superconducting properties. The existence of such structural inhomogeneities brings into question whether exotic experimental results obtained from superconducting materials with high transition temperatures actually reflect intrinsic properties.