The kinetic analysis of any isothermal process is based on compliance with the equational form g(alpha) = kt, which requires an a priori knowledge of the final property change Delta p(infinity). It is therefore imperative that this equation is not applied to incomplete reactions. A new on-line method has therefore been developed here which gives analytical solutions to well known mechanisms of reaction without recourse to Delta p(infinity). In some cases, where Delta p(infinity)k appears as a product or exponential terms are to be found, computer based numerical methods have been adopted to solve the equations. The deciphering of the mechanism and the evaluation of k without waiting for the completion of a TG run has been demonstrated with a hypothetical TG curve.