We present second-harmonic generation experiments in p-doped asymmetri
cally stepped quantum wells using the emission of a free-electron lase
r in the wavelength interval between 13 and 18 mu m. The wells are des
igned such that the three fewest valence-subbands are about equally sp
aced. We measured the angular and frequency dependence of the second-h
armonic signal excited by intense laser irradiation chosen to be nearl
y resonant with the transitions between the three lowest valence subba
nds. We see evidence of the optical second-order susceptibility compon
ents 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.