  We consider a cosmological model in which the two major fluid components of
the Universe, dark energy and dark matter, flow with distinct four-velocities.
This cosmological configuration is equivalent to a single anisotropic fluid,
expanding with a four-velocity that is an appropriate combination of the two
fluid four-velocities. The energy density of the single cosmological fluid is
larger than the sum of the energy densities of the two perfect fluids, i.e.,
dark energy and dark matter, respectively, and contains a correction term due
to the anisotropy generated by the differences in the four-velocities.
Furthermore, the gravitational field equations of the two-fluid anisotropic
cosmological model are obtained for a Bianchi type I geometry. By assuming that
the non-comoving motion of the dark energy and dark matter induces small
perturbations in the homogeneous and isotropic
Friedmann-Lemaitre-Robertson-Walker type cosmological background, and that the
anisotropy parameter is small, the equations of the cosmological perturbations
due to the non-comoving nature of the two major components are obtained. The
time evolution of the metric perturbations is explicitly obtained for the cases
of the exponential and power law background cosmological expansion. Therefore,
if there is a slight difference between the four-velocities of the dark energy
and dark matter, the Universe would acquire some anisotropic characteristics,
and its geometry will deviate from the standard FLRW one. In fact, the recent
Planck results show that the presence of an intrinsic large scale anisotropy in
the Universe cannot be excluded {\it a priori}, so that the model presented in
this work can be considered as a plausible and viable working hypothesis.
