We present a simulation of the OH stretching band in the gas-phase IR spectra of strongly hydrogen-bonded dimers of phosphinic acid and their deuterated analogs [(R2POOH(D), with R = CH2Cl, CH3], which is based on a model for a centrosymmetric hydrogen-bonded dimer that treats the high-frequency OH stretches harmonically and the low-frequency intermonomer (i.e., O center dot center dot center dot O) stretches anharmonically. This model takes into account the following effects: anharmonic coupling between the OH and O center dot center dot center dot O stretching modes; Davydov coupling between the two hydrogen bonds in the dimer; promotion of symmetry-forbidden OH stretching transitions; Fermi resonances between the fundamental of the OH stretches and the overtones of the in- and out-of-plane bending modes involving the OH groups; direct relaxation of the OH stretches; and indirect relaxation of the OH stretches via the O center dot center dot center dot O stretches. Using a set of physically sound parameters as input into this model, we have captured the main features in the experimental OH(D) bands of these dimers. The effects of key parameters on the spectra are also elucidated. By increasing the number and strength of the Fermi resonances and by promoting symmetry-forbidden OH stretching transitions in our simulations, we directly see the emergence of the ABC structure, which is a characteristic feature in the spectra of very strongly hydrogen-bonded dimers. However, in the case of the deuterated dimers, which do not exhibit the ABC structure, the Fermi resonances are found to be much weaker. The results of this model therefore shed light on the origin of the ABC structure in the IR spectra of strongly hydrogen-bonded dimers, which has been a subject of debate for decades.