  Commensurability oscillations in the magnetoresistivity of a two-dimensional
electron gas in a two-dimensional lateral superlattice are studied in the
framework of quasiclassical transport theory. It is assumed that the impurity
scattering is of small-angle nature characteristic for currently fabricated
high-mobility heterostructures. The shape of the modulation-induced
magnetoresistivity $\Delta\rho_{xx}$ depends on the value of the parameter
$\gamma\equiv \eta^2 ql/4$, where $\eta$ and $q$ are the strength and the wave
vector of the modulation, and $l$ is the transport mean free path. For
$\gamma\ll 1$, the oscillations are described, in the regime of not too strong
magnetic fields $B$, by perturbation theory in $\eta$ as applied earlier to the
case of one-dimensional modulation. At stronger fields, where $\Delta\rho_{xx}$
becomes much larger than the Drude resistivity, the transport takes the
advection-diffusion form (Rayleigh-B\'enard convection cell) with a large
P\'eclet number, implying a much slower ($\propto B^{3/4}$) increase of the
oscillation amplitude with $B$. If $\gamma\gg 1$, the transport at low $B$ is
dominated by the modulation-induced chaos (rather than by disorder). The
magnetoresistivity drops exponentially and the commensurability oscillations
start to develop at the magnetic fields where the motion takes the form of the
adiabatic drift. Conditions of applicability, the role of the type of disorder,
and the feasibility of experimental observation are discussed.
