  Let $k$ be a number field and $X$ a smooth integral affine variety equipped
with a morphism $f : X \to A^1_k$ to the affine line. Assume that all fibres of
$f$ are split, for instance that they are geometrically integral. Assume that
the generic fibre of $f$ is a homogeneous space of a simply connected, almost
simple, semisimple group $G/k(t)$, and that the geometric stabilizers are
connected reductive groups. Let $v$ be a place of $k$ such that the fibration
$f$ acquires a rational section over the completion $k_v$ at $v$. Assume
moreover that at almost all points $x \in A^1(k_v)$ the specialized group $G_x$
is isotropic over $k_v$. If the Brauer group of $X$ is reduced to the Brauer
group of $k$, then strong approximation holds for $X$ away from the place $v$.
