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In this paper, the "relative" version of semi-projectivity is considered.Let M and N be modules.N is called M-semi-projective, if any homomorphism from N to an M-cycllc submodule f(M) of N can be factored through to a homomorphism from N to M and f, where f ∈[M, N].Some properties of relative semi-projectivity are obtained.Next, we consider a wider class of "relatively semi-projective" modules such as "relatively direct-projective" modules which were introduced by Nicholson and Zhou.Several properties of their homomorphisms are also obtained.