  In this paper, we discuss hypercontractivity for the Markov semigroup $P_t$
which is generated by segment processes associated with a range of functional
SDEs of neutral type. As applications, we also reveal that the semigroup $P_t$
converges exponentially to its unique invariant probability measure $\mu$ in
entropy, $L^2 (\mu)$ and $\|\cdot\|_{\mbox{var}}$, respectively.
