We consider here two approaches to the planning of experiments when one must take into account the possibility of the unadequacy of the assumed model. We restrict ourselves with the simpliest cases of one-dimensional polynomial and trigonometric regressions. At first we find that the D-optimal designs are appropriate when one wishes to minimize the average of the quadratic divergion from the true model even when applying incorrect model. The other part of the paper is devoted to the designs maximizing the power of F-test for checking the significance of some coefficients.