The nonlinear breakage equations are a mathematical model for the dynamics
of cluster growth when clusters undergo binary collisions resulting either
in coalescence or breakup with possible transfer of matter. Each of these
two events may happen with an a priori prescribed probability depending for
instance on the sizes of the colliding clusters. The model consists of a
countable number of non-locally coupled nonlinear ordinary differential
equations modeling the concentration of the various clusters. In the
present paper we consider asymptotic behavior of solutions as time tends
to infinity and prove the weak* convergence to steady states provided at
least two monoclusters appear after a collision, and the weak* convergence
to some equilibrium state at the expense of making stronger assumptions.
A result on the strong convergence has also been obtained.