The results of studies of the conductivity and critical current density of single-crystal films Nd2− xCexCuO4+δ /SrTiO3 with an axis c perpendicular or parallel to the substrate plane with a cerium concentration of x = 0.15 and x = 0.17 are presented. It was found that in the stoichiometrically annealed films with the optimum cerium content (x = 0.15) the resistance anisotropy is maximal and the anisotropy of the critical current density is jcab/jcc ≅ 3 103 at T = 4.2 K . The strong anisotropy of the critical current density is considered within the framework of the natural superlattices with alternating conducting CuO2 layers and nonconducting Nd(Ce)O-buffer layers. It was found that the high density of the critical current along the conducting CuO2 planes is related to the pinning of vortices on the buffer layers and a strong anisotropy of the critical current density is a manifestation of the anisotropic motion of the vortex lattice in a layered superconductor. © 2019 Institute for Low Temperature Physics and Engineering. All Rights Reserved.