  We consider the Bianchi I geometry coupled to several species of comoving
barotropic perfect fluids with a linear equation of state in the context of
general relativity. The solution of the dynamics can be reduced to a
quadrature, which can be explicitly performed in certain cases. In particular,
we obtain the explicit solution for one species, as well as for two species,
given their barotropic indices obey certain relation. These solutions include
and generalize different models studied in the literature. For completeness, we
analyze all the different possible signs of the matter energy densities, and we
obtain a particularly interesting model in which an exotic species produces a
bounce of the scale factor, providing a singularity-free cosmology, and then
decays to leave a nonexotic component as the dominant fluid for large volumes.
