  Recent studies have revealed that for the majority of species the length
distributions of duplicated sequences in natural DNA follow a power-law tail.
We study duplication-mutation models for processes in natural DNA sequences and
the length distributions of exact matches computed from both synthetic and
natural sequences. Here we present a hierarchy of equations for various number
of exact matches for these models. The reduction of these equations to one
equation for pairs of exact repeats is found. Quantitative correspondence of
solutions of the equation to simulations is demonstrated.
