  We present a family of exact rotating anisotropic fluid solutions, which
satisfy all energy conditions for certain values of their parameters. The
components of the Ricci tensor $R_{\mu\nu}$ the eigenvalues of the tensor
$R_\mu^\nu$ and the energy-momentum tensor $T_{\mu\nu}$ of the solutions are
given explicitly. All members of the family have the ring singularity of Kerr's
solution and most of them one or two more singularities. The solutions can be
matched to the solution of Kerr on three closed surfaces, which for proper
values of the parameters of the solutions approximate oblate spheroids. All
matching surfaces are thin shells. For some values of a constant the surface
density in one of them is positive everywhere and in this surface and in its
interior all energy conditions are satisfied.
