Let G be a multigraph, g and f be integer-valued functions defined on V( G). Then a graph G is called a ( g, f)-graph if g( x)≤ degG( x)≤ f( x) for each x∈ V( G), and a ( g, f)-factor is a spanning ( g, f)-subgraph. If the edges of graph G can be decomposed into ( g, f)-factors, then we say that G is ( g, f)-factorable. In this paper, we obtained some sufficient conditions for a graph to be ( g, f)-factorable. One of them is the following: Let m be a positive integer, l be an integer with l= m (mod 4) and 0≤ l≤3. If G is an -graph, then G is ( g, f)-factorable. Our results imply several previous ( g, f)-factorization results. [ABSTRACT FROM AUTHOR]