In this paper we consider the robust stability problem for a neutral delay-differential system where the characteristic equations involve a polytope of quasi-polynomials. First, the ’Edge theorem’ is developed for robust stability analysis of a polytope of neutral quasi-polynomials. Based on the Edge theorem, the robust stability of neutral systems with commensurate delays will be reduced to the checking of the H (Hurwitz)-stability of all the edges of a polytope of quasi-polynomials and the Schur stability of all the edges of the subpolytope of neutral terms. Then, an effective graphical test is made for checking the robust stability of a polytope of neutral quasi-polynomials. Finally, we show that checking vertic quasi-polynomials is sufficient for the asymptotic stability of the entire family of first-order quasi-polynomials of the neutral type.