  We theoretically predict instability of a zero-dc-current state of the
two-dimensional electron system formed on the surface of liquid helium induced
by the cyclotron resonance (CR). This conclusion follows from the theoretical
analysis of the dc magnetoconductivity which takes into account the
contribution from radiation in an exact way. A many-electron model of the
dynamic structure factor of the 2D Coulomb liquid is used to describe the
influence of strong internal forces acting between electrons. For low electron
densities and high amplitudes of the microwave field, the dc
magnetoconductivity is shown to become negative in the vicinity of the CR which
causes the instability. This effect is strongly suppressed by Coulomb forces in
the region of high densities.
