Stability Polynomials characterize the propagation behaviour of the error vectors associated with the numerical solution of differential equations. It is desirable that these polynomials extend as far as possible along the negativex-axis in a strip of width 2. This can be achieved by appropriately determining the coefficients of the polynomial which are largely at our disposal. In the case of one step methods the problem can be reduced to an approximation problem. By applying a modifiedRemez algorithm the optimal coefficients are computed. It is shown that the optimal stability polynomials are generalizedChebyshev polynomials.