The N-H stretching vibrations of adenine, one of the building blocks of DNA, are studied by combining infrared absorption and nonlinear two-dimensional infrared spectroscopy with ab initio calculations. We determine diagonal and off-diagonal anharmonicities of N-H stretching vibrations in chemically modified adenosine monomer dissolved in chloroform. For the single-quantum excitation manifold, the normal mode picture with symmetric and asymmetric NH(2) stretching vibrations is fully appropriate. For the two-quantum excitation manifold, however, the interplay between intermode coupling and frequency shifts due to a large diagonal anharmonicity leads to a situation where strong mixing does not occur. We compare our findings with previously reported values obtained on overtone spectroscopy of coupled hydrogen stretching oscillators.