  We consider two models of interacting DNA molecules: \textit{First} is (four
parametric) bubble coalescence model in interacting DNAs (shortly: BCI-DNA).
\textit{Second} is (three parametric) bubble coalescence model in a condensed
DNA molecules (shortly BCC-DNA). To study bubble coalescence thermodynamics of
BCI-DNA and BCC-DNA models we use methods of statistical physics. Namely, we
define Hamiltonian of each model and give their translation-invariant Gibbs
measures (TIGMs). For the first model we find parameters such that
corresponding Hamiltonian has up to three TIGMs (three phases of system)
biologically meaning existence of three states: ``No bubble coalescence'',
``Dominated soft zone'', ``Bubble coalescence''. For the second model we show
that for any (admissible) parameters this model has unique TIGM. This is a
state where ``No bubble coalescence'' phase dominates.

Statistical Mechanics