|| The identification or model building of system is the important problem for the dynamic optimization of chemical plant and it is desired that this mathematical model can be determined as quickly and as exactly as possible from experimental or operating data. Recently the identification of linear system has been studied, but there have been few papers on nonlinear systems. Especially, no approaches can be found to identify effectively a chemical reaction process which is a nonlinear and nonisothermal system. Except for the case in which the linearized model is enough to represent the approximate dynamic behaviour of the plant, system should be directly represented by nonlinear mathematical model in general. In this paper, the gradient method was applied to identify a nonlinear system. In this method, the parameters to be chosen optimally are regarded as timeinvariant control variables and they are numerically determined by using a high speed digital computer (KDC-I). As a numerical example, we choose a continuous stirred tank reactor with the first order exothermic reaction and show the procedure to determine the three parameters, that is, the order of reaction, the values of activation energy and frequency factor. It should be emphasized that this approach makes it possible to construct the mathematical model of nonisothermal chemical reaction processes only from input and output data.