An extension of stimulus-sampling theory is provided for the two-response case where the response is given continuously in time and the reinforcements are given according to some time-dependent process. The particular instance of a Poisson-type noncontingent reinforcement schedule is thoroughly examined. The generalized axioms on which the theory is based are stated and fundamental equations derived. Comparisons between this theory and the discrete-trial theory are provided, with emphasis on the similarities and differences between the results. Some sequential statistics are derived, and the results of a pilot experiment are briefly reported.