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Longitudinal optical (LO) phonon relaxation is investigated in a GaAs/AlGaAs triple barrier tunnel diode at strong perpendicular magnetic fields. We observe LO‐phonon assisted tunneling to the ground state as well as to Landau level states. Maxima in the LO‐phonon assisted tunnel peak are found each time the LO‐phonon energy matches multiple of the Landau level spacing. Corresponding maxima as well as parity effects are found in the integral tunnel conductance. The results indicate enhancement of LO‐phonon assisted inter Landau level transitions with increasing magnetic field. © 1996 American Institute of Physics.