  We develop a systematic theory of the Hall effect in Q1D conductors in both
weak and strong magnetic fields for a model where the electron relaxation time
varies over the Fermi surface. At high temperatures, the Hall coefficient
saturates at the value $-\beta/ecn$, where the dimensionless coefficient
$\beta$ is determined by the curvature of the longitudinal dispersion law of
electrons, $e$ the electron charge, $c$ is the speed of light, and $n$ is the
hole concentration. At low temperatures, where a strong variation of the
relaxation rate over the Fermi surface develops in the form of ``hot spots'',
the Hall coefficient becomes temperature-dependent and may change sign for a
particular choice of the transverse dispersion law parameters. In our model,
the sign changes in a weak, but not in a strong magnetic field.
