  Recently, Dreyer and Duderstadt have proposed a modification of the
Becker--Doering cluster equations which now have a nonconvex Lyapunov function.
We start with existence and uniqueness results for the modified equations. Next
we derive an explicit criterion for the existence of equilibrium states and
solve the minimization problem for the Lyapunov function. Finally, we discuss
the long time behavior in the case that equilibrium solutions do exist.
