The question of whether a molecule can be made to absorb and emit photons only in groups of n is treated. Pulse sequences are introduced which in effect selectively induce the absorption of only groups of n photons. This causes only n-quantum transitions even when many other transitions might be resonant. The technique involves repeated phase shifts of 2π/n in the radiation to build up the selected coherences and cancel all other coherences, and is applicable to a wide range of spectroscopic systems. Coherent averaging theory is extended to describe selective sequences and demonstrates that n-quantum selectivity is possible to arbitrarily high order in the average Hamiltonian expansion. High-order selectivity requires many phase shifts, however, and for this reason the residual nonselective effects of sequences which are selective to only a finite order are calculated. Selective sequences are applied to the multiple-quantum NMR of oriented molecules, where in combination with time reversal sequences they produce a much more efficient transfer of the population differences into selected coherences than is obtainable by normal wideband pumping. For example, the 10-quantum transition in a 10-spin system can be enhanced by more than four orders of magnitude. Experiments on selective excitation of the 4-quantum transitions in oriented benzene verify the expected enhancement. © 1980 American Institute of Physics.