Minimax robust designs are studied for regression models with possible misspecified response functions. These designs, minimizing the maximum of the mean squared error matrix, can control the bias caused by model misspecification and the desired efficiency through one parameter. Using nonsmooth optimization technique, we derive the minimax designs analytically for misspecified regression models. This extends the results in Heo, Schmuland and Wiens (2001). Several examples are discussed for approximately polynomial regression. / Graduate