  In this article, we study obstructions to weak approximation for connected
linear groups and homogeneous spaces with connected or abelian stabilizers over
finite extensions of $\mathbb C((x,y))$ or function fields of curves over
$\mathbb C((t))$. We show that for connected linear groups, the usual
Brauer-Manin obstruction works as in the case of tori. However, this
Brauer-Manin obstruction is not enough for homogeneous spaces, as shown by the
examples we give. We then construct an obstruction using torsors under
quasi-trivial tori that explains the failure of weak-approximation.
