A digraph D is supereulerian if D has a spanning directed eulerian subdigraph. We give a necessary condition for a digraph to be supereulerian first and then characterize the digraph D which are not supereulerian under the condition that 1092831d80d237b486c0fc446e82e" title="Click to view the MathML source">未+(D)+未−(D)≥|V(D)|−4.