The existence of nonsuperconducting zones in YBa2Cu3O7−δ (YBCO) films below the transition temperature to the nonresistive state can limit the performances of YBCO devices. In this work, we present detailed measurements of the temperature dependence of the critical surface current density of c-axis oriented epitaxial YBCO films, that suggest that their superconducting critical temperature, Tc, is modulated along the c-axis. This nonuniformity of Tc, that could be present in all YBCO films, seems also to be supported by measurements of both the field cooled in-plane magnetic moment and the oxygen content (by non-Rutherford elastic resonance scattering) of some samples.