Abstract A theory is developed which treats in a unified way the many different aspects of the problems of the resonant excitation of a high-lying atomic or molecular state by the absorption of n photons from up to n different lasers. It is assumed that no intermediate states are resonantly excited. The effects of saturation, Stark shifts, spontaneous emission, and finite laser bandwidths are included. In the general case the formalism reduces to a set of equations analogous to the Bloch equations. In special circumstances the formalism reduces further to rate equations or to simple single or double integrals: in these cases Doppler broadening is included as well. The domains in which each of the formalisms is appropriate are carefully defined and various asymptotic cases presented.