  Let X be a homogeneous space of a connected linear algebraic group G' over a
number field k, containing a k-point x. Assume that the stabilizer of x in G'
is connected. Using the notion of a quasi-trivial group, recently introduced by
Colliot-Th\'el\`ene, we can represent X in the form X=G/H, where G is a
quasi-trivial k-group and H is a connected k-subgroup of G. Let S be a finite
set of places of k. Applying results of [B2], we compute the defect of weak
approximation for X with respect to S in terms of the biggest toric quotient T
of H. In particular, we show that if T splits over a metacyclic extension of k,
then X has the weak approximation property. We show also that any homogeneous
space X with connected stabilizer (without assumptions on T) has the real
approximation property.
