In this work, we use the Hadamard representation of polynomials and several known results on the stability of polynomial families to describe new polynomial families which are stable under substitutions. Such polynomial families can be seen as nonlinear stable perturbations of ‘small-in-parameters’ polynomials. Also, the stability condition can be obtained of the positive definitness of certain Bezoutians associated with the even and odd parts of the resulting polynomial families. Some implications of our results for control analysis and design are discussed. Copyright © 2000 John Wiley & Sons, Ltd.