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The human respiratory response to breathing an excess of carbon dioxide gas is modeled on physiological grounds as an almost linear second-order system. The parameters corresponding to the gains, time constants, threshold, and noise powers are identified by both least squares and maximum likelihood methods. The purpose is both to find the site of action of drugs and to gain understanding of this part of the respiratory control system. It is concluded that the maximum likelihood method is necessary in cases where the noise is not white and when unbiased estimates of the gains and variances are essential, such as in drug studies and in some physiological modeling.