Branched DNA structures include several DNA regions connected by three- or four-way DNA junctions. Branched DNAs can be intermediates in DNA replication and recombination in living organisms and in sequence-specific DNA targeting in vitro. Branched DNA structures are usually metastable and irreversibly dissociate to non-branched products via a DNA strand exchange process commonly known as DNA branch migration. The key parameter in the DNA dissociation process is its characteristic time, which depends on the length of the dissociating DNA structure. Here, we predict that the presence of a slow reversible initiation step, which precedes DNA branch migration, can alter, to almost linear dependence, the ?classic? quadratic dependence of the dissociation time on the length of the dissociating DNA structure. This prediction can be applied to dissociation of Y-like DNA structures and double D-loop DNA hybrids, which are DNA structures similar to replication bubbles. In addition, the slow initiation step can increase the effect of DNA sequence heterologies within the structure on its kinetic stability. Applications of our analysis for genetic manipulations with branched DNA structures are discussed.