  We provide a relation between Brauer-Manin obstruction and descent
obstruction for torsors over open varieties under a connected linear algebraic
group or a group of multiplicative type is given. Such a relation is further
refined for torsors under a torus. As an appliaction, we prove that the
semi-simple part of a connected linear algebraic group will satisfy strong
approximation with Brauer-Manin obstruction if G iteself satisfies strong
approximation with Brauer-Manin obstruction.The equivalence between descent
obstruction and etale Brauer-Manin obstruction for smooth projective varieties
is extended to smooth quasi-projective varieties, which provides the
perspective to study integral points.
