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We present second-harmonic generation experiments in p-doped asymmetrically stepped quantum wells using the emission of a free-electron laser in the wavelength interval between 13 and 18 mu m. The wells are designed such that the three fewest valence-subbands are about equally spaced. We measured the angular and frequency dependence of the second-harmonic signal excited by intense laser irradiation chosen to be nearly resonant with the transitions between the three lowest valence subbands. We see evidence of the optical second-order susceptibility components chi(xxz)((2)), chi(zxx)((2)) and chi(zxy)((2)), chi(xyz)((2)) in the quantum wells and determine their enhancement with respect to chi(xyz)((2)) of bulk GaAs.