  We report on a new class of magnetoresistance oscillations observed in a
high-mobility two-dimensional electron gas (2DEG) in GaAs-Al$_x$Ga$_{1-x}$As
heterostructures. Appearing in a weak magnetic field ($B<$ 0.3 T) and only in a
narrow temperature range (2 K $<T<$ 9 K), these oscillations are periodic in
1/B with a frequency proportional to the electron Fermi wave vector, $k_F$. We
interpret the effect as a magnetophonon resonance of the 2DEG with leaky
interface-acoustic phonon modes carrying a wave vector $q=2k_F$. Calculations
show a few branches of such modes on the GaAs-Al$_x$Ga$_{1-x}$As interface, and
their velocities are in quantitative agreement with the data.
