  A generalized two-component model with peakon solutions is proposed in this
paper. It allows an arbitrary function to be involved in as well as including
some existing integrable peakon equations as special reductions. The
generalized two-component system is shown to possess Lax pair and infinitely
many conservation laws. Bi-Hamiltonian structures and peakon interactions are
discussed in detail for typical representative equations of the generalized
system. In particular, a new type of $N$-peakon solution, which is not in the
traveling wave type, is obtained from the generalized system.
