Tunneling processes between subbands in two independently contacted two-dimensional electron-gas systems on a GaAs-Al x Ga 1− x As-GaAs heterostructure were investigated. The theoretical results obtained by self-consistent calculations are in excellent agreement with the values for the subband energies determined by tunneling spectroscopy. If a magnetic field is applied perpendicular to the planes of the sample, additional structures in the derivative of the current-voltage characteristics are identified as tunneling processes between different Landau levels on both sides of the barrier. With in-plane magnetic fields, the conservation of the canonical momentum results in a very large broadening of the subband resonances. As a consequence, the mean values of the wave functions, even for unoccupied subbands, can be directly determined.