We prove that stable numerical finite difference methods for first-order hyperbolics, which use s forward and r backward steps in the discretization of the space derivatives, are of order at most 2 min{r+1, s}. This generalizes results of Strang (1964) and of Engquist & Osher (1980b). We also derive linear stability results for interpolatory finite differences. The given analysis is based on a generalization of the theory of order stars.