AbstractWe show that a strongly connected digraph with n vertices and minimum degree ⩾ n is pancyclic unless it is one of the graphs Kp,p. This generalizes a result of A. Ghouila-Houri. We disprove a conjecture of J. A. Bondy by showing that there exist hamiltonian digraphs with n vertices and 12n(n + 1) – 3 edges which are not pancyclic. We show that any hamiltonian digraph with n vertices and at least 12n(n + 1) – 1 edges is pancyclic and we give some generalizations of this result. As applications of these results we determine the minimal number of edges required in a digraph to guarantee the existence of a cycle of length k, k ⩾ 2, and we consider the corresponding problem where the digraphs under consideration are assumed to be strongly connected.