  We discuss classical magnetotransport in a two-dimensional system with strong
scatterers. Even in the limit of very low field, when $\omega_c \tau \ll 1$
($\omega_c$ is the cyclotron frequency, $\tau$ is the scattering time) such a
system demonstrates strong negative magnetoresistance caused by non-Markovian
memory effects. A regular method for the calculation of non-Markovian
corrections to the Drude conductivity is presented. A quantitative theory of
the recently discovered anomalous low-field magnetoresistance is developed for
the system of two-dimensional electrons scattered by hard disks of radius $a,$
randomly distributed with concentration $n.$ For small magnetic fields the
magentoresistance is found to be parabolic and inversely proportional to the
gas parameter, $ \delta \rho_{xx}/\rho \sim - (\omega_c \tau)^2 / n a^2.$ In
some interval of magnetic fields the magnetoresistance is shown to be linear
$\delta \rho_{xx}/\rho \sim - \omega_c \tau $ in a good agreement with the
experiment and numerical simulations. Magnetoresistance saturates for $\omega_c
\tau \gg na^2$, when the anomalous memory effects are totally destroyed by the
magnetic field. We also discuss magnetotransport at very low fields and show
that at such fields magnetoresistance is determined by the trajectories having
a long Lyapunov region.
