  We present femtosecond pump-probe measurements of the nondegenerate
(1960$\,$nm excitation and 1176--1326$\,$nm probe) two-photon absorption
spectra of 8 $\,$nm GaAs/12$\,$nm Al$_{0.32}$Ga$_{0.68}$As quantum well
waveguides. Experiments were performed with light pulses co-polarized normal
and tangential to the quantum well plane. The results are compared to
perturbative calculations of transition rates between states determined by the
$\mathbf{k}\cdot\mathbf{p}$ method with an 8 or 14 band basis. We find
excellent agreement between theory and experiment for normal polarization, then
use the model to support predictions of orders-of-magnitude enhancement of
nondegenerate two-photon absorption as one constituent photon energy nears an
intersubband resonance.
