We study the behaviour of trajectories of real homeomorphisms h. There are exactly 15 order types among them. For each h let \(T_h\) be the collection of all order types of h-trajectories. This \(T_h\) will be called a package (of order types). We prove that \( \mid T_h\mid \le 11\) always. As h varies over the set of all homeomorphisms from \({\mathbb {R}}\) to \({\mathbb {R}}\) , we ask how many sets can arise as \(T_h\) ? We prove that the answer is exactly 36. An example is given at the end to show how these packages are helpful for conjugacy classification.
