  In an earlier paper we developed the classification of weakly symmetric
pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$
is a reductive subgroup. We derived the classification from the cases where $G$
is compact. As a consequence we obtained the classification of semisimple
weakly symmetric manifolds of Lorentz signature $(n-1,1)$ and trans--lorentzian
signature $(n-2,2)$. Here we work out the classification of weakly symmetric
pseudo--riemannian nilmanifolds $G/H$ from the classification for the case $G =
N\rtimes H$ with $H$ compact and $N$ nilpotent. It turns out that there is a
plethora of new examples that merit further study. Starting with that
riemannian case, we see just when a given involutive automorphism of $H$
extends to an involutive automorphism of $G$, and we show that any two such
extensions result in isometric pseudo--riemannian nilmanifolds. The results are
tabulated in the last two sections of the paper.
