  Electrons in monolayer graphene in the presence of an electromagnetic (or
electric) wave are considered theoretically. It is shown that the electron
motion is a nonlinear combination of Zitterbewegung (ZB, trembling motion)
resulting from the periodic potential of graphene lattice and the driving field
of the wave. This complex motion is called "Multi-mode Zitterbewegung". The
theory is based on the time-dependent two-band Hamiltonian taking into account
the graphene band structure and interaction with the wave. Our theoretical
treatment includes the rotating wave approximation and high-driving-frequency
approximation for narrow wave packets, as well as numerical calculations for
packets of arbitrary widths. Different regimes of electron motion are found,
depending on relation between the ZB frequency $\omega_Z$ and the driving
frequency $\omega_D$ for different strengths of the electron-wave interaction.
Frequencies and intensities of the resulting oscillation modes are calculated.
The nonlinearity of the problem results in a pronounced multi-mode behavior.
Polarization of the medium is also calculated relating our theoretical results
to observable quantities. The presence of driving wave, resulting in
frequencies directly related to $\omega_Z$ and increasing the decay time of
oscillations, should facilitate observations of the Zitterbewegung phenomenon.
