The statistics of time-resolved photon detection in single-molecule continuous-excitation fluorescence spectroscopy is examined for three-and two-state models of a dye molecule. A unified description is provided in terms of stationary stochastic point processes. The pair distribution function and the distribution of interdetection times are related to the parameters of the models, and explicit expressions are given for the two-state model. The effect of the detected background is taken into account. Based on an analysis of tripler blinking, we argue that time-resolved photon detection offers an alternative to fluorescence intensity spectroscopy in unravelling the underlying single-molecule processes.