We have investigated resistive properties of a-axis YBa₂Cu₃O₇/a,b-axis PrBa₂Cu₃O₇ superlattices in magnetic fields to study thermally activated flux-flow resistance. We find that in magnetic fields perpendicular to the YBa₂Cu₃O₇/PrBa₂Cu₃O₇ layering the activation energies of these superlattices deduced from the tail of the resistive transitions have a logarithmic magnetic-field dependence for small YBa₂Cu₃O₇ thicknesses (<300 Å), in agreement with recent theories of thermally activated resistance in strongly pinned two-dimensional superconductors.