Let h be a nonnegative integer. The h-restricted edge connectivity λh(G) of a simple connected graph G is defined as the minimum cardinality over the sets of edges of G, if any, whose removal disconnects G and every component of the resulting graph has more than h vertices. This paper gave a necessary and sufficient condition and also three useful sufficient conditions to guarantee the existence of λh(G). Moreover, it explicitly characterized the graphs whose 2-restricted edge connectivities do not exist.