Recently the possibilistic linear models whose coefficients are fuzzy parameters have been proposed by Tanaka et al. The features of this model are to be able to deal with fuzzy data and to represent a fuzzy relation between input and output variables. In this paper, we extend the possibilistic linear models to nonlinear interval models in order to analyze the complex system using interval data. This extension is achieved by proposing the interval GMDH. Two interval regression models are obtained by this method. One model is obtained so as to include interval data. Thus interval data are included in the intervals estimated by this model. Another model is obtained so as to be included in interval data. Thus interval data include the intervals estimated by this model. Interval data from grinding experiments of fine ceramics by diamond grinding wheels are analyzed to illustrate the proposed method.