The problem of matching a given input-output behavior for systems described by general nonlinear differential equations is considered. It is shown that, by appropriately modifying the zero-dynamics algorithm, it is possible to obtain a simple, necessary, and sufficient condition for the solvability of the model matching problem, which requires that the initial state be on an appropriate submanifold of the state space. Another condition necessary and sufficient for the solvability of the strong model matching problem is proposed. This last condition is then related to an equality of a list of integers which, under some regularity assumptions, coincide with the algebraic structures at infinity of the process and of a composition of the process and the model. The relation between these conditions and the equality of the algebraic structures at infinity of the process and the model is established. >