  Functions of several octonion variables are investigated and integral
representation theorems for them are proved. With the help of them solutions of
the ${\tilde {\partial}}$-equations are studied. More generally functions of
several Cayley-Dickson variables are considered. Integral formulas of the
Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are
proved in the new generalized form for functions of Cayley-Dickson variables
instead of complex. Moreover, analogs of Stein manifolds over Cayley-Dickson
graded algebras are defined and investigated.
