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.