  We consider diffusion-limited reactions A_i + A_j -> 0 (1 <= i < j <= q) in d
space dimensions. For q > 2 and d >= 2 we argue that the asymptotic density
decay for such mutual annihilation processes with equal rates and initial
densities is the same as for single-species pair annihilation A + A -> 0. In d
= 1, however, particle segregation occurs for all q < oo. The total density
decays according to a $q$ dependent power law, rho(t) ~ t^{-\alpha(q)}. Within
a simplified version of the model \alpha(q) = (q-1) / 2q can be determined
exactly. Our findings are supported through Monte Carlo simulations.
