  In this paper, we look at the extention of Hedlund's characterization of
cellular automata to the case of cellular automata in the hyperbolic plane.
This requires an additionnal condition. The new theorem is proved with full
details in the case of the pentagrid and in the case of the ternary heptagrid
and enough indications to show that it holds also on the grids $\{p,q\}$ of the
hyperbolic plane.
