Summary: In this paper, it is shown that \((\mathcal{V},\mathfrak{X})\) is a Schur pair if and only if the Baer-invariant of an \(\mathfrak{X}\)-group with respect to \(\mathcal{V}\) is an \(\mathfrak{X}\)-group. Also, it is proved that a locally \(\mathfrak{X}\) class inherited the Schur pair property of, whenever \(\mathfrak{X}\) is closed with respect to forming subgroup, images and extensions of its members. Subsequently, many interesting predicates about some generalizations of Schur’s theorem and Schur multiplier of groups will be concluded.