In this paper one begins to studi cyclic hypergroupoids. In particular, in the finite case, by using the set C_x= \{n\in N^* | x^{(n+1)}\subseteq \bigcup_{k=1}^n x^{(k)} \} and the maximum element of the set N-C_x, one characterizes the structure of the cyclic subhypergroupoid <x> generated by x.
