In the chemical and petrochemical industries kinetic models are useful for describing the physical and chemical steps that occur in commercial processes. Often kinetic models involve several responses. Box and Draper (1965) have demonstrated that using multiresponse data for estimating the parameters in a model results in confidence regions for the parameters that are smaller than those obtained when the responses are considered individually, and they have developed a procedure for the multiresponse estimation of common parameters. Using multiresponse data also provides a better understanding of the reaction mechanism and makes possible a more comprehensive assessment of the correctness of the proposed model. Data from an oil shale pyrolysis experiment was used to fit and critique a sequence of models. These showed that conversion of the organic material in shale to oil was better explained when an intermediate product was included in the reaction network, and multiresponse techniques were employed. This led to a plausible kinetic representation of the pyrolysis process. Multiresponse models for more complex reaction mechanisms may require the estimation of a large number of parameters. An example is given, methods for minimizing computational difficulties in this situation are discussed, and some numerical results are presented.