  We study the coherent dynamics of relaxing qubits driven by a bichromatic
radiation in the dispersive regime, when detuning of the frequency
$\omega_{rf}$ of a longitudinal radiofrequency field from the Rabi frequency
$\omega_{1}$ in a transverse microwave field is comparable in magnitude to
$\omega_{rf}$ and $\omega_{1}$. We analytically describe this regime beyond the
rotating wave approximation and find that the dominant feature of dynamics of
qubits is the shift of the Rabi frequency caused by the dynamical Zeeman and
Bloch-Siegert-like effects. These fundamental effects can be experimentally
separated because, unlike the Bloch-Siegert effect, the dynamical Zeeman effect
depends on the detuning sign. Our theoretical results are in a good agreement
with the experimental data obtained in pulse EPR for the $E'_{1}$ centers in
crystalline quartz.
