  We investigate the kinetics of many-species systems with aggregation of
similar species clusters and annihilation of opposite species clusters. We find
that the interplay between aggregation and annihilation leads to rich kinetic
behaviors and unusual conservation laws. On the mean-field level, an exact
solution for the cluster-mass distribution is obtained. Asymptotically, this
solution exhibits a novel scaling form if the initial species densities are the
same while in the general case of unequal densities the process approaches
single species aggregation. The theoretical predictions are compared with
numerical simulations in 1D, 2D, and 3D. Nontrivial growth exponents
characterize the mass distribution in one dimension.
