  Let $G$ be a connected semisimple group over an algebraically closed field
$k$ of characteristic 0. Let $Y=G/H$ be a spherical homogeneous space of $G$,
and let $Y'$ be a spherical embedding of $Y$. Let $k_0$ be a subfield of $k$.
Let $G_0$ be a $k_0$ -model ($k_0$-form) of $G$. We show that if $G_0$ is an
inner form of a split group and if the subgroup $H$ of $G$ is spherically
closed, then $Y$ admits a $G_0$-equivariant $k_0$-model. If we replace the
assumption that $H$ is spherically closed by the stronger assumption that $H$
coincides with its normalizer in $G$, then $Y$ and $Y'$ admit compatible
$G_0$-equivariant $k_0$-models, and these models are unique.
