Quantum calculations are used to analyse the nature and strength of binding of complexes pairing H2X with the HXX radical, X=S,O, with particular interest in the comparison of S with O. Complexes are cyclic in the sense that each subunit acts simultaneously as both proton donor and acceptor in a pair of H-bonds. Binding energies vary from 3 kcal mol-1 for H2S ··· HSS to a maximum of 7 kcal mol-1 for H2O ··· HOO; intermediate values of about 4 kcal mol-1 are obtained for structures where only one subunit contains S. Analysis of geometric, vibrational, and electronic data indicate that the XXH ··· XH2 H-bond is considerably stronger than HXH ··· XXH in which the radical serves as proton acceptor, and that HOO is a more potent proton donor than HSS.