Quantum calculations are used to analyze the nature and strength of binding of complexes pairing aliphatic amines with the HO and HOO radicals, with particular emphasis on the comparison of HO with HOO. Complexes are stabilized by N⋯HO(O) H-bonds involving the N lone pair. The OOH radical binds more strongly in all cases than does OH, and shows a longer stretch of its OH bond, as well as a greater red shift of this bond’s stretching frequency. MP2/6-311++G(3df, 3pd) binding energies vary from 28 kJ/mol for CH3NH2⋯HO to a maximum of 56 kJ/mol for (CH3)2NH⋯HOO. The reliability of a new hybrid meta exchange-correlation functional, M05-2X, compares favorably with MP2, generally better than B3LYP.