We have derived equations, by employing [U-¹³C]glucose and mass isotopomer analysis, to determine the pathways of glycogen synthesis (J. Katz, W. P. Lee, P. A. Wals, and E. A. Bergner. J. Biol. Chem. 264: 12994-13004, 1989). More recently, by use of these methods we have derived equations to determine the rate of glucose recycling and of gluconeogenesis [Tayek and Katz. Am. J. Physiol. 270 (Endocrinol. Metab. 33): E709-E717, 1996 and 272 (Endocrinol. Metab. 35): E476-E484, 1997, and Katz and Tayek. Am. J. Physiol. 275 (Endocrinol. Metab. 38): E537-E542, 1988]. The former equations have been criticized and challenged by C. Des Rosiers, B. R. Landau, and H. Brunengraber [Am. J. Physiol. 259 (Endocrinol. Metab. 22): E757-E762, 1990], and the latter recently by B. R. Landau, J. Wahren, S. F. Previs, G. K. Ekberg, D. Yang, and H. Brunengraber [Am. J. Physiol. 274 (Endocrinol. Metab. 37): E954-E961, 1998]. Landau et al. claimed that our equations were in error and "corrected" them. Their analysis, and their values for recycling and gluconeogenesis (GNG) differ markedly from ours. We show here our equations and estimates of recycling and GNG to be correct. We present here a theoretical analysis of recycling and discuss the determination of the Cori Cycle and GNG. We illustrate by numerical examples the difference in parameters of glucose metabolism calculated by the methods of Katz and Landau. J. Radziuk and W. N. P. Lee [Am. J. Physiol. 277 (Endocrinol Metab. 40): E199-E207, 1999] and J. K. Kelleher [Am. J. Physiol. 277 (Endocrinol. Metab. 40): E395-E400, 1999] present a mathematical analysis that, although differing in some respects from Landau's, supports his equation for GNG. We show in the APPENDIX that their derivation of the equation for GNG is incorrect.