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We consider two models of interacting DNA molecules: \textit{First} is (fourparametric) bubble coalescence model in interacting DNAs (shortly: BCI-DNA).\textit{Second} is (three parametric) bubble coalescence model in a condensedDNA molecules (shortly BCC-DNA). To study bubble coalescence thermodynamics ofBCI-DNA and BCC-DNA models we use methods of statistical physics. Namely, wedefine Hamiltonian of each model and give their translation-invariant Gibbsmeasures (TIGMs). For the first model we find parameters such thatcorresponding 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 showthat for any (admissible) parameters this model has unique TIGM. This is astate where ``No bubble coalescence'' phase dominates.

Bubble coalescence in interacting system of DNA molecules