  In this work we are interested in the general problem of the determination of
the normed division algebras. Our fundamental results are obtained in the
particular subclass of those 8-dimensional quadratic flexible real division
algebras.
  We give a new process which generalizes that of Cayley-Dickson and which
allows the obtaining of a new family of eight-dimensional quadratic flexible
real division algebras. We give examples of 8-dimensional quadratic flexible
real division algebras which cannot be obtained by this first process of
duplication and by means of a second process, which consists in making an
appropriate deformation of the product of the octonion algebra, we determine
these last ones and we resolve the isomorphism problem. Among the
eight-dimensional quadratic flexible real division algebras, we study those
which possess a nontrivial derivation by mean of the generalized Cayley-Dickson
process. We also give examples where the group of automorphisms is trivial, and
characterize the algebras whose group of automorphisms is not trivial. This
brings to light the unlimitedness of this subclass of algebras.
