  We extend the loop algebra construction for algebras graded by abelian groups
to study graded-simple algebras over the field of real numbers (or any real
closed field). As an application, we classify up to isomorphism the
graded-simple alternative (nonassociative) algebras and graded-simple
finite-dimensional Jordan algebras of degree 2. We also classify the
graded-division alternative (nonassociative) algebras up to equivalence.
