  In this paper we consider Positive Definite functions on products
$\Omega_{2q}\times\Omega_{2p}$ of complex spheres, and we obtain a condition,
in terms of the coefficients in their disc polynomial expansions, which is
necessary and sufficient for the function to be Strictly Positive Definite. The
result includes also the more delicate cases in which $p$ and/or $q$ can be $1$
or $\infty$.
  The condition we obtain states that a suitable set in $\mathbb{Z}^2$,
containing the indexes of the strictly positive coefficients in the expansion,
must intersect every product of arithmetic progressions.
