  A semiclassical theory for magnetotrasport in a quantum Hall system near
filling factor $\nu = 1/2 $ based on the Composite Fermions physical picture is
used to analyze the effect of local flattening of the Composite Fermion Fermi
surface (CF-FS) upon magnetoacoustic oscllations. We report on calculations of
the velocity shift and attenuation of a surface acoustic wave (SAW) which
travels above the two-dimensional electron system, and we show that local
geometry of the CF-FS could give rise to noticeable changes in the magnitude
and phase of the oscillations. We predict these changes to be revealed in
experiments, and to be used in further studies of the shape and symmetries of
the CF-FS. Main conclusions reported here could be applied to analyze
magnetotransport in quantum Hall systems at higher filling factors $ \nu = 3/2,
5/2 $ provided the Fermi-liquid-like state of the system.
