The model proposed by Steele (Ann. NY Acad. Sci. 82: 420-430, 1959) to compute rates of appearance and disappearance in non-steady state is subjected to theoretical analysis. It is shown that this model introduces an error with two components, one dependent on the volume of the compartment, the other related to the complex configuration of the system. The errors depend on the time course of specific activity, change differently with time, and may take the opposite sign but they do not, in general, cancel each other. Corollaries of this analysis are the following: there is no single pool-fraction value satisfactory under all non-steady-state situations; keeping tracer specific activity as constant as possible during the experiment minimizes both errors; and non-steady-state analysis demands proper modeling of the system. Tracer experiments were carried out in five normal volunteers. Plasma [3-3H]glucose concentration was first brought to equilibrium by means of a primed constant 2-h infusion, and then the steady state was perturbed by a 2-h euglycemic insulin (1 mU X min-1 X kg-1) clamp, realizing a transition between a basal and a euglycemic hyperinsulinemic steady state. These data were analyzed with Steele's equation, the two compartment models of Radziuk et al. [Am. J. Physiol. 234 (Endocrinol. Metab. Gastrointest. Physiol. 3): E84-E93, 1978], and a new model based on a study on glucose kinetics carried out in the two steady states separately. Steele's equation yielded negative values for hepatic glucose production already 40 min into the clamp and throughout the study. The average value of glucose production during the 2nd h was -0.88 mg X min-1 X kg-1; the suppression of basal release over the 2-h period was 115%. In contrast, the new model calculated a mean glucose production of 0.37 mg X min-1 X kg-1 during the 2nd h and an overall suppression of 62%; no negative values were obtained.