  Since the Lorentz force is perpendicular to the magnetic field, it should not
affect the motion of a charge along the field. This argument seems to imply
absence of longitudinal magnetoresistance (LMR) which is, however, observed in
many materials and reproduced by standard semiclassical transport theory
applied to particular metals. We derive a necessary and sufficient condition on
the shape of the Fermi surface for non-zero LMR. Although an anisotropic
spectrum is a pre-requisite for LMR, not all types of anisotropy can give rise
to the effect: a spectrum should not be separable in any sense. More precisely,
the combination $k_{\rho}v_{\phi}/v_{\rho}$, where $k_\rho$ is the radial
component of the momentum in a cylindrical system with the z-axis along the
magnetic field and $v_{\rho} (v_{\phi}$) is the radial (tangential) component
of the velocity, should depend on the momentum along the field. For some
lattice types, this condition is satisfied already at the level of
nearest-neighbor hopping; for others, the required non-separabality occurs only
if next-to-nearest-neighbor hopping is taken into account.
