Singlet states with lifetimes that are longer than spin-lattice relaxation times TS > T1 offer unique opportunities for studying very slow dynamic processes in solution-state NMR. A set of novel experiments can achieve broadband excitation of singlet states in pairs of coupled spins. The most elaborate of these experiments, two-dimensional singlet-state exchange spectroscopy (SS-EXSY), is independent of the offsets of the two spins, their relative chemical shifts, and their scalar couplings. The new methods open the way to study very slow chemical exchange or translational diffusion using mixing times taum = Ts >> T1. The lifetimes TS of singlet states of pairs of protons in a partially deuterated saccharide are shown to be longer than the longitudinal proton relaxation times T1 in the same compound by a factor of ca. 37.