Abstract: The study of centralizers of elements in an algebraic group is very important from the point of view of structure theory. It was proved by Steinberg that there are only finitely many conjugacy classes of centralizers over algebraically closed field. Floyd and Mostow proved that if a compact Lie group acts on a compact manifold then there are only finitely many orbit types. In view of this, we indicate that the result of Steinberg is indeed true for anisotropic algebraic groups over R for several class of groups. In particular we sketch the proof for groups of type G₂.