  In the present paper the macroscopic limits of the kinetic model for
inter-acting entities (individuals, organisms, cells) are studied. The kinetic
model is one-dimensional and entities are characterized by their position and
orientation (+/-) with swarming interaction controlled by the sensitivity
parameter. The macroscopic limits of the model are considered for solutions
close either to the diffusive (isotropic) or to the aligned (swarming)
equilibrium states for various sensitivity parameters. In the former case the
classical linear difusion equation results whereas in the latter a traveling
wave solution does both in the zeroth (`Euler') and frst (`Navier-Stokes')
order of approximation.
