  Let X be a rational nonsingular compact connected real algebraic surface.
Denote by Aut(X) the group of real algebraic automorphisms of X. We show that
the group Aut(X) acts n-transitively on X, for all natural integers n. As an
application we give a new and simpler proof of the fact that two rational
nonsingular compact connected real algebraic surfaces are isomorphic if and
only if they are homeomorphic as topological surfaces.
