Summary: The notion of strongly regular modules over a ring which is not necessarily commutative is introduced. The relation between \(F\)-regular, \(GF\)-regular and \(vn\)-regular modules that are defined over commutative rings and strongly regular module is obtained. We have shown that a remark that if \(R\) is a reduced ring, then the \(R\)-module \(M\) is \(F\)-regular if and only if \(M\) is \(GF\)-regular is false. We have obtained the necessary and sufficient condition under which the remark is true. We have shown that if \(R\) is a commutative ring and if \(M\) is finitely generated multiplication module then the notion of \(F\)-regular, \(GF\)-regular, \(vn\)-regular and strongly regular are equivalent.