  We study Weyssenhoff spin fluids in Bianchi type-I cosmological models,
within the framework of torsional f(R)-gravity; the resulting field equations
are derived and discussed in both Jordan and Einstein frames, clarifying the
role played by the spin and the non-linearity of the gravitational Lagrangian
f(R) in generating the torsional dynamical contributions. The general
conservation laws holding for f(R)-gravity with torsion are employed to provide
the conditions needed to ensure the preservation of the Hamiltonian constraint
and the consequent correct formulation of the associated initial value problem.
Examples are eventually given.
