  We analyze the long time behavior of initial value problems that model a
process where particles of type A and B diffuse in some substratum and react
according to $nA+nB\to C$. The case n=1 has been studied before; it presents
nontrivial behavior on the reactive scale only. In this paper we discuss in
detail the cases $n>3$, and prove that they show nontrivial behavior on the
reactive and the diffusive length scale.
