We analyze the kinetics of a pigment system with thermal and photochemical transitions among its states. The general mathematical description is obtained and is then specialized to systems with two stable states (states with negligible thermal outlets) in which the total amount of pigment is conserved. We describe the properties of the pigment state populations and of their kinetics in not-too bright lights. The wavelength dependence of the population distribution following saturating light is called the saturation spectrum. The populations are shown to relax to this saturation distribution exponentially with amount of light; the wavelength dependence of the relaxation constant is called the relaxation spectrum. The specialized description of the pigment kinetics is applied to the six-state, two-stable-state model of Minke et al. (1974) for the barnacle visual pigment. The immediate spur for this analysis was a problem which has recently become acute: That of deciding between a single bistable pigment system and two separate systems as the possible origin of various abnormally-shaped or nonmatching action or absorption spectra or wavelengthdependent response forms which have been observed in many invertebrate photoreceptors. We show that these two possibilities may be distinguished quite generally by saturation and relaxation measurements, and describe such measurements in the following article.