  We analyze a class of models for unequal crossover (UC) of sequences
containing sections with repeated units that may differ in length. In these,
the probability of an `imperfect' alignment, in which the shorter sequence has
d units without a partner in the longer one, scales like q^d as compared to
`perfect' alignments where all these copies are paired. The class is
parameterized by this penalty factor q. An effectively infinite population size
and thus deterministic dynamics is assumed. For the extreme cases q=0 and q=1,
and any initial distribution whose moments satisfy certain conditions, we prove
the convergence to one of the known fixed points, uniquely determined by the
mean copy number, in both discrete and continuous time. For the intermediate
parameter values, the existence of fixed points is shown.
