  The kinetic theory is formulated with respect to anholonomic frames of
reference on curved spacetimes. By using the concept of nonlinear connection we
develop an approach to modelling locally anisotropic kinetic processes and, in
corresponding limits, the relativistic non-equilibrium thermodynamics with
local anisotropy. This lead to a unified formulation of the kinetic equations
on (pseudo) Riemannian spaces and in various higher dimensional models of
Kaluza-Klein type and/or generalized Lagrange and Finsler spaces. The
transition rate considered for the locally anisotropic transport equations is
related to the differential cross section and spacetime parameters of
anisotropy. The equations of states for pressure and energy in locally
anisotropic thermodynamics are derived. The obtained general expressions for
heat conductivity, shear and volume viscosity coefficients are applied to
determine the transport coefficients of cosmic fluids in spacetimes with
generic local anisotropy. We emphasize that such locally anisotropic structures
are induced also in general relativity if we are modelling physical processes
with respect to frames with mixed sets of holonomic and anholonomic basis
vectors which naturally admits an associated nonlinear connection structure.
