An {\it oriented cycle} is an orientation of a undirected cycle.We first show that for any oriented cycle $C$, there are digraphs containing no subdivision of $C$ (as a subdigraph) and arbitrarily large chromatic number.In contrast, we show that for any $C$ is a cycle with two blocks, every strongly connected digraph with sufficiently large chromatic number contains a subdivision of $C$. We prove a similar result for the antidirected cycle on four vertices (in which two vertices have out-degree $2$ and two vertices have in-degree $2$).Un {\it cycle orienté} est l'orientation d'un cycle. Nous prouvons que pour tout cycle orienté $C$ il existe des graphes dirigés sans subdivisions de $C$ (en tant que sous graphe) et de nombre chromatique ar...