  We predict a double-resonant feature in the magnetic field dependence of the
phonon-mediated longitudinal conductivity $\sigma_{xx}$ of a two-subband
quasi-two-dimensional electron system in a quantizing magnetic field. The two
sharp peaks in $\sigma_{xx}$ appear when the energy separation between two
Landau levels belonging to different size-quantization subbands is favorable
for acoustic-phonon transitions. One-phonon and two-phonon mechanisms of
electron conductivity are calculated and mutually compared. The phonon-mediated
interaction between the intersecting Landau levels is considered and no avoided
crossing is found at thermal equilibrium.
