  In this paper, we investigate stability in distribution of neutral stochastic
functional differential equations with infinite delay (NSFDEwID) at the state
space
  \begin{equation*}
  C_{r}=\{{\varphi\in
C((-\infty,0];R^{d}):\|\varphi\|_{r}=\sup_{-\infty<\theta\leq0}e^{r\theta}\lvert\varphi(\theta)\rvert}
< \infty\ , \quad r > 0 \}.
  \end{equation*}
  We drive a sufficient strong monotone condition for the existence and
uniqueness of the global solutions of NSFDEwID in the state space $ C_{r} $. We
also address the stability of the solution map $ x_{t} $ and illustrate the
theory with an example.
