In this paper, we consider identified directed networks where processes know an upper bound on the maximum ancestor distance. Under these settings, we study the conditions on the network topology allowing the self-stabilization of two fundamental problems: the leader election and the synchronous unison. Precisely, we show that those two problems can be self-stabilizingly solved in our settings if and only if the network contains a unique source component. In particular, to show that our condition is sufficient, we propose two algorithms and study their complexity. Notice that our topological condition covers a wide spectrum of digraphs since, for example, strongly connected digraphs, dipaths, and out-trees have a unique source component.