  We investigate spreading properties of solutions of a large class of
two-component reaction-diffusion systems, including prey-predator systems as a
special case. By spreading properties we mean the long time behaviour of
solution fronts that start from localized (i.e. compactly supported) initial
data. Though there are results in the literature on the existence of travelling
waves for such systems, very little has been known-at least theoretically-about
the spreading phenomena exhibited by solutions with compactly supported initial
data. The main difficulty comes from the fact that the comparison principle
does not hold for such systems. Furthermore, the techniques that are known for
travelling waves such as fixed point theorems and phase portrait analysis do
not apply to spreading fronts. In this paper, we first prove that spreading
occurs with definite spreading speeds. Intriguingly, two separate fronts of
different speeds may appear in one solution-one for the prey and the other for
the predator-in some situations.
