This paper deals with robustness properties of a control system subject to parameter uncertainty when the parameters appear affine multilinearly in the coefficients of the characteristic polynomial. The robust Hurwitz stability of such a multilinear interval polynomial family reduces to that of the stability of a set of manifolds derived from the Kharitonov polynomials. Several extremal properties of these stability manifolds are derived. These properties are useful in determining the worst case parametric, H(infinity) and nonlinear sector bounded stability margins for control systems containing interval parametric uncertainty. They generalize previous results obtained by the authors for the linear case.