  The exact solution of the asymmetric exclusion problem with particles of
first and second class is presented. In this model the particles (size 1) of
both classes are attached on lattice points and diffuse with equal asymmetric
rates, but particles in the first class do not distinguish those in the second
class from the holes (empty sites). We generalize and solve exactly this model
by considering molecules in the first and second class with sizes $s_1$ and
$s_2$ ($s_1,s_2 = 0,1,2,...$), in units of lattice spacing, respectively. The
solution is derived by a Bethe ansatz of nested type. We give in this paper a
pedagogical and simple presentation of the Bethe ansatz solution of the problem
which can easily be followed by a non specialized audience in exactly
integrable models.
