Tournaments and Orders with the Pigeonhole Property A binary structure $S$ has the pigeonhole property ($\mathcal{P}$) if every finite partition of $S$ induces a block isomorphic to $S$. We classify all countable tournaments with ($\mathcal{P}$); the class of orders with ($\mathcal{P}$) is completely classified. Keywords:pigeonhole property, tournament, orderCategories:05C20, 03C15