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In this paper we consider the category M-FQMod of M-fuzzy (left) Q-modules over a given quantale Q. We introduce and investigate the notion of M-fuzzy Q-submodule of a left Q-module. Also, the notions of M-fuzzy module nuclei and conuclei on a left Q-module are defined, and the elementary properties of both are studied. The relationships between such notions and M-fuzzy Q-submodule are discussed. Finally, the relationship between the category of M-fuzzy Q-modules and the category of (L, M)-quasi-fuzzy topological spaces is discussed. [ABSTRACT FROM AUTHOR]