  {\small \ We generalize the concepts of \thinspace level \thinspace and
\thinspace sublevel of a composition algebra to division algebras obtained by
the Cayley-Dickson process. In 1967, R. B. Brown constructed, for every}$t\in
\mathbb{N},${\small \ a nonassociative division algebra}$A_{t}${\small \ of
dimension}$2^{t}${\small \ over the power-series
field}$K\{X_{1},X_{2},...,X_{t}\}.\,${\small \ This gives us the possibility to
construct a division algebra of \thinspace dimension}$% {\small
\,2}^{t}\,${\small and prescribed \thinspace level and sublevel}$% {\small
\,\,2}^{k}${\small ,\thinspace \thinspace}$k,\,t\in \mathbb{N}-\{0\} $ and
dimension ${\small \,2}^{t}\,${\small and prescribed \thinspace level}${\small
\,\,2}^{k}+1${\small ,\thinspace \thinspace}$k\in \mathbb{N}% -\{0\},t\in
\mathbb{N},t\geq 2.$
