A critical examination is made of the mathematical principles that are used for the kinetic interpretation of nonisothermal thermoanalytical rate measurement by a representative approximate method, the widely applied Coats-Redfern (CR) equation. It is concluded that the dominant feature in the identification of that isothermal kinetic equation, which most satisfactorily expresses the rate characteristics, is the (effective) exponent in the set of equations comparatively considered. Consequently, the form of the CR equation possesses only limited ability to distinguish between 'fits' to alternative kinetic models. This is entirely consistent with literature conclusions expressing the view that data from a single nonisothermal experiment is insufficient to identify the three kinetic parameters: kinetic model, g(alpha) = kt, and both Arrhenius terms, A and E.An usual first step in kinetic analysis by the CR (and other related) equations is to incorporate the kinetic model (g(alpha) = kt) into the expression used to calculate A and E. Because the rate equation (effective) exponent is a dominant and, without supporting observations, is an unknown parameter, this introduces the well-known ambiguity that alternative kinetic parameters are obtained by the uncritical use of this method.Accordingly, the following replacement calculation sequence is recommended as being more trustworthy. At least two. preferably several. nonisothermal experiments are undertaken, each at a different (usually constant) rate of temperature increase. For a comprehensive range of constant increments of reaction, Deltaalpha(i), the different rates (dalpha/dt) at different reaction temperatures, T-i. are determined from the several experiments and the activation energy, E-i, for each successive reaction interval can be calculated. The constancy, or otherwise, of E-i with alpha(i) throughout the reaction is thus established. From these data, the rate constant for each alpha(i) value can be extrapolated to a selected representative temperature T-R, perhaps at the mid-point of a reaction (alpha = 0.5). From these data a pseudoisothermal alpha-t (T-R constant) curve can be constructed, suitable for analysis by the usual methods. Various advantages from this approach are perceived. The unfortunate role of the (effective) kinetic model exponent in combination with the logarithmic form of the CR equation in analyzing the data, which inhibits recognition of the kinetic model, is avoided. The laborious calculations will not be a problem for modem high-speed computers, unlike the situation existing when the CR equation was first introduced in 1964. Suitable programs may be used to maximize the accuracy of the method, through the use of several nonisothermal experiments and small Deltaalpha increments in the analysis. Kinetic comparisons can be extended to a wider range of kinetic models than the limited selection that often restrict the possibilities for nonisothermal rate data interpretation by the most widely used approximate methods. (C) 2003 Elsevier B.V. All rights reserved.