In this computational work we study complexes with two equivalent intermolecular hydrogen bonds formed between trimethyl phosphine oxide and two identical proton donors ("twin" hydrogen bonds) for a set of 70 proton donor molecules. The changes in the phosphorus chemical shift and stretching frequency of the PO group upon complexation correlate quite well with the total strength of two hydrogen bonds. A set of explicit numerical dependences is proposed for assessing interatomic distances and hydrogen bond strengths from spectral data. Comparison with the results obtained for analogous previously studied 1 : 1 complexes allowed us to analyze in detail anticooperativity effects on the geometry, energy and spectral parameters. Two hydrogen bonds compete for the PO acceptor group and their mutual weakening increases nonlinearly with the strengthening of the complex, reaching approximately 25% in energy (which corresponds to 0.1 Å lengthening for short strong H-bonds), which is clearly seen in NMR and IR spectra and correlates well with the changes in the spectral parameters.