Controversy over the use of rectilinear plots for the interpretation of isotopic rock lead studies has prompted the following analysis of discrete two‐ and three‐stage episodic models, which is partly in the nature of a review, but which also introduces some new results. An investigation is made of the restrictive conditions under which these models lead to rectilinear plots in the isochron, lead‐lead, and modified concordia diagrams; the question of the solubility of these models and the possibility of discriminating between them are discussed. It is shown that there are two special three‐stage models that lead to rectilinear plots in all diagrams and that one of these models cannot (from uranium‐lead data alone) be distinguished from the two‐stage model. The alternative special rectilinear three‐stage model, which can be distinguished both from the two‐stage and from other three‐stage models on the basis of uranium‐lead data alone, cannot be fully solved on the basis of these data alone. The necessity of using data other than the uranium‐lead data (such as the ‘age of the earth’ or the duration of the last stage of lead evolution) either to solve or to distinguish the models makes it clear that a fully independent age of the earth cannot be derived from uranium‐lead data alone. A discussion is also given of the solubility of general three‐ and four‐stage models by use of ‘age‐corrected’ isotope ratios to correct back one stage. It is shown that careless application of a particular multistage model without proper investigation of its consistency with the data can lead to false interpretations. Recent controversy over the use of multistage models is discussed; much of the controversy is shown to arise out of a confusion of the models with the particular diagram used to plot the data. In general no one diagram is to be preferred to another, with the exceptions that ifµ1is variable the modified concordia diagram must be used, whereas the discussion of age‐corrected isotope ratios necessitates use of the lead‐lead diagram. A brief discussion is given of the interpretation of oceanic lead data, for which the analytical precision at present may often be insufficient for the proper application of consistency tests; individual sets of oceanic lead therefore are not susceptible of unambiguous interpretation at this time. It is emphasized that this real lack of information cannot be overcome (as has been implied in some papers) by the use of alternative presentations of the data. The new Tera‐Wasserburg diagram is examined, as is the recently introduced idea that the initial207Pb/206Pb ratio may serve as an important chronometer for early planetary system evolution. Both ideas are shown to contribute no information that cannot be derived from the modified concordia diagram. The application of the Tera‐Wasserburg diagram in the attempt to derive from lunar basalt U‐Pb data an independent age of the moon is shown to rest on precisely the same principles and to be subject to the same restrictions and uncertainties as earlier attempts to derive an age of the earth from terrestrial oceanic basalts. A discussion is also given of the question of homogenization and of the application o