Optimization of warfarin administration was achieved theoretically using a mathe matical model for dose- patient dynamics. The criterion for optimization is to mini mize the time necessary to obtain the desired prothrombin levels . The patient model consists of linear and non-linear parts connected sequentially . The linear part is simply the 2- compartment model. The non-linear part is an exponential function of the linear part's output, which represents the time- independent relation between the serum dose density and the prothrombin time. The parameters in these models were identified for the mean values of the clinical data. By the discrete-time system theory, i. e. the finite time settling method, the optimal administration strategy was achieved for this patient model. The result agrees fairly closely with the empirical optimization.