An analysis is presented of the transverse resonant tunneling transport through GaAs/AlGaAs superlattices due to tunneling between Landau levels in quantum wells in a strong tilted magnetic field. A high tunneling rate is demonstrated between Landau levels with Δn ≠ 0 in a magnetic field with a nonzero in-plane component. This leads to substantial broadening and shift of the tunneling resonance and significant changes in the current-voltage characteristics of superlattices. The predicted behavior of the current-voltage characteristics of superlattices in tilted magnetic fields is demonstrated experimentally.