  We present a theory of magnetooscillations around the $\nu =1/2$ Landau level
filling factor based on a model with a fluctuating Chern--Simons field. The
quasiclassical treatment of the problem is appropriate and leads to an
unconventional $\exp\left[-(\pi/\omega_c\tau^*_{1/2})^4\right]$ behavior of the
amplitude of oscillations. This result is in good qualitative agreement with
available experimental data.
