In an attempt to generalize Christofides algorithm for metric TSP to the asymmetric TSP with triangle inequality we have studied various properties of directed spanning cacti. In this paper we first observe that finding the TSP in a directed, weighted complete graph with triangle inequality is polynomial time equivalent to finding the minimum spanning cactus in the graph and then prove that it is NP-complete to determine whether a general unweighted digraph contains a directed spanning cactus. The proof is a reduction from Exact cover and may be of independent interest.