Three non-parametric models are presented for describing the survival experience of patients with chronic disease. Model I assumes that two independent forces of mortality (disease specific and normal) act simultaneously on the total patient population. If after a number of intervals the observed survival experience approximates a normal level, a cure rate can be estimated and the survival pattern described according to Model II: a c-fraction subject only to normal mortality and a (1–c)-fraction subject to an additional mortality risk. If the observed survival appears to be stabilizing at a level somewhat lower than normal, the data fit Model III: a c′-fraction subject to a mortality risk somewhat higher than normal, and a (1–c′)-fraction subject to a high additional mortality risk. When there is no evidence of stabilization of interval survival rates, no cure rate can be estimated and only Model I is applicable. Models I and II can be considered as special cases of Model III. Comparisons are made with the parametric model proposed by Berkson and Gage. The usefulness of mathematical models is determined by the extent to which they provide insight into the “natural history of the disease” and by the extent to which they provide clinically meaningful formulations for the evaluation of treatment.