  We present a general formulation to calculate the dynamic optical
conductivity, beyond the linear response regime, of any electronic system whose
quasiparticle dispersion is described by a two band model. Our phenomenological
model is based on the optical Bloch equations. In the steady state regime it
yields an analytic solution for the population inversion and the interband
coherence, which are nonlinear in the optical field intensity, including finite
doping and temperature effects. We explicitly show that the optical
nonlinearities are controlled by a single dimensionless parameter which is
directly proportional to the incident field strength and inversely proportional
to the optical frequency. This identification leads to a unified way to study
the dynamical conductivity and the differential transmission spectrum across a
wide range of optical frequencies, and optical field strength. We use our
formalism to analytically calculate the nonlinear optical conductivity of doped
and gapped graphene, deriving the well known universal ac conductivity of
$\sigma_0={e^2}/4\hbar$ in the linear response regime of low optical
intensities (or equivalently high frequencies) and non-linear deviations from
it which appear at high laser intensities (or low frequencies) including the
impact of finite doping and band-gap opening.
