  Microwave-induced nonlinear magnetoresistance in a dc-driven two-dimensional
electron system is examined using a multi-photon-assisted transport scheme
direct controlled by the current. It is shown that near the 2nd subharmonic of
the cyclotron resonance, the frequency of the resistivity oscillation with the
magnetic-field-normalized current-density is double that at the cyclotron
resonance and its harmonics, in excellent agreement with recent experimental
findings by Hatke {\it et al.} [Phys. Rev. Lett. {\bf 101}, 246811 (2008)]. The
current-induced alternative emergence of resonant two-photon and single-photon
processes is responsible for this frequency doubling. Near the third
subharmonic of the cyclotron resonance, the current-induced consecutive
appearance of resonant 0-/3-photon, two-photon, and single-photon processes may
lead to the frequency tripling of the resistivity oscillation.
