  In classical kinetic or kinetic-like models a particle free path distribution
is exponensial, but this is more likely to be an exception than a rule. In this
paper we derive a linear Boltzmann-like equation for a general free path
distribution in the framework of Alt's model J. Math. Biol. 9:147 (1980). In
the special case that the free path distribution has at least first and second
finite moments we construct an asymptotic solution of the equation for small
mean free paths. The asymptotic solution becomes a diffusion approximation to
the one-speed Boltzmann-like equation.
