  We study invariance and monotonicity properties of Kunita-type stochastic
differential equations in $\RR^d$ with delay. Our first result provides
sufficient conditions for the invariance of closed subsets of $\RR^d$. Then we
present a comparison principle and show that under appropriate conditions the
stochastic delay system considered generates a monotone (order-preserving)
random dynamical system. Several applications are considered.
