Assume that $\varphi: (R,\fm) \longrightarrow (S,\fn)$ is a local flat homomorphism between commutative Noetherian local rings $R$ and $S$. Let $M$ be a finitely generalized $R-$module. The ascent and descent of generalized sequentially Cohen-Macaulayness between $R-$module $M$ and $S-$module $M\otimes_RS$ are given. An example is given to point out that the result of M. Tousi and S. Yassemi \cite{TY} can not be extended for generalized sequentially Cohen-Macaulay modules.

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