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Let R be a commutative ring with identity and M be unitary R-module. Let M and N be two R-modules, M is called pseudo-N- injective if for each R-submodule K of N , and each R-monomorphism from K, into M, can be extended to an R-homomorphism from N into M, M is called pseudo-injective if M is pseudo -M-injective. And M is called essentially- pseudo-N- injective, if for any essential R-submodule A of N and any R-monomorphism from A into M can be extended to R-homomorphism from N into M. M is called essentially pseudo- injective, if M is essentially- pseudo-M- injective. The purpose of this work is to give a comprehensive study of essentially-pseudo-N- injective modules, and we supply the details of the proofs for most of the results that were given by Alahmadi an Jain. We add also some results that seem to be new to the best of our knowledge. Among these results are the following: Every pseudo- injective CS-module is continuous. If M is essentially- pseudo-N- injective R-module, then M is essentially- pseudo-K- injective R-module for every essential R-submodule K of N. Isomorphic R-module to essentially- pseudo-N- injective R-module is essentially- pseudo-N- injective for any R-module N. If M is essentially- pseudo-N_1- injective R-module and N_1 and N_2 are two isomorphic R-modules, then M is essentially- pseudo-N_2- injective R-module. Any direct summand of essentially- pseudo-N- injective R-module is essentially- pseudo-N- injective. If M is essentially- pseudo-N- injective R-module, then for any R-monomorphism α:M→N with α(M) is essential submodule of N, there exists an R-homomorphismβ:N→M such that β∘α=I. If M is uniform module, then M is essentially- pseudo- injective if and only if M is pseudo- injective module. If M is monophorm module, then M is essentially- pseudo- injective if and only if M is quasi-injective module. Every essential fully invariant submodule of essentially- pseudo- injective module is essentially- pseudo- injective. 10-If M is essentially- pseudo- injective multiplication R- module, then every essential submodule of M is essentially pseudo- injective.
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