  Sufficient and necessary conditions are presented for the order-preservation
of stochastic functional differential equations on $\R^d$ with non-Lipschitzian
coefficients driven by the Brownian motion and Poisson processes. The
sufficiency of the conditions extends and improves some known comparison
theorems derived recently for one-dimesional equations and multidimensional
equations without delay, and the necessity is new even in these special
situations.
