We describe a new type of sufficient condition for a digraph to be Ham
iltonian. Conditions of this type combine local structure of the digra
ph with conditions on the degrees of nonadjacent vertices. The main di
fference from earlier conditions is that we do not require a degree co
ndition on all pairs of nonadjacent vertices. Our results generalize t
he classical conditions by Ghouila-Houri and Woodall. (C) 1996 John Wi
ley & Sons, Inc.