  The linear transports along paths in vector bundles introduced in Ref. [1]
are applied to the special case of tensor bundles over a given differentiable
manifold. Links with the transports along paths generated by derivations of
tensor algebras are investigated. A possible generalization of the theory of
geodesics is proposed when the parallel transport generated by a linear
connection is replaced with an arbitrary linear transport along paths in the
tangent bundle.
