Summary: Let \(G\) be a multiplicative group. Let \(R\) be a \(G\)-graded commutative ring and \(M\) a \(G\)-graded \(R\)-module. Various properties of graded prime submodules and graded primary submodules of \(M\) are discussed. We also discuss the graded radical of graded submodules of multiplication graded \(R\)-modules.