In this paper we characterize the boundary partial derivative f(B) of the image f(B) of a box B in R(m) under a nonlinear mapping f:R(m) --> C. We generalize results recently reported by Polyak and Kogan (1993) [Necessary and Sufficient Conditions for Robust Stability of Multiaffine Systems. Mathematics Research Report 93-06, University of Maryland Baltimore County] for multiaffine mappings, and provide computationally tractable necessary and sufficient robust stability conditions for quasipolynomials with interval coefficients and interval delays. A numerical stability verification for a quasipolynomial family with two interval delays is presented.