A general quantum theoretical approach of the νX-H IR line shape of cyclic dimers of weakly H-bonded species in the gas phase is proposed. In this model, the adiabatic approximation (allowing to separate the high frequency motion from the slow one of the H-bond bridge), is performed for each separate H-bond bridge of the dimer and a strong nonadiabatic correction is introduced into the model via the resonant exchange between the fast mode excited states of the two moieties. The present model reduces satisfactorily to many models in the literature dealing with more special situations. It has been applied to the cyclic dimers (CD3CO2H)2 and (CD3CO2D)2 in the gas phase. It correctly fits the experimental line shape of the hydrogenated compound and predict satisfactorily the evolution in the line shapes, to the deuterated one by reducing simply the angular frequency of the H-bond bridge and the anharmonic coupling parameter by the factor 1/√2 .