Let τ = (T , F) be a torsion theory. An R-module M is τ-lifting, if for any submodule N of M there exists a decomposition M = A ⊕ B such that A ≤ N and N ∩ B is τ-small in M. This definition unifies several definitions on generalizations of lifting property of modules. In the present paper, various results on τ-lifting modules are developed, many extending known results.
