Summary: In this paper, we establish the relationship between the relative \(L\)-order (relative \(L^\ast\)-order), relative \(L\)-type (relative \(L^\ast\)-type) and relative \(L\)-weak type (relative \(L^\ast\)-weak type) of a transcendental meromorphic function \(f\) with respect to an transcendental entire function \(g\) and that of monomial generated by the meromorphic \(f\) and entire \(g\).