Abstract: Let G be a graph, and let g and f be integer-valued functions defined on V(G) such that g(x)≤ f(x) for all x∈ V(G). A graph G is called a (g,f,H)-extendable ifafter deleting the vertices of any subgraph which is isomorphic to H the remaining subgraph of G has a (g,f)-factor. In the
paper the characterization of (g,f,H)-extendable graph is given. Furthermore, the properties of (g,f,n)-extendable graph(H=nK₁) are studied.

Key words: (g,f)-factor, (g,f,H)-extendable graph