Epitaxial thin films of the heavy fermion superconductor UNi2Al3 with Tc(max)=0.98 K were investigated. The transition temperature Tc depends on the current direction which can be related to superconducting gaps opening at different temperatures. Also the influence of the magnetic ordering at TN approximately 5 K on R(T) is strongly anisotropic, indicating different coupling between the magnetic moments and itinerant charge carriers on the multisheeted Fermi surface. The upper critical field Hc2(T) suggests an unconventional spin-singlet superconducting state.