  A product of K\"ahler manifolds also carries a K\"ahler metric. In this short
note we would like to study the product of generalized $p-$K\"ahler manifolds,
compact or not. The results we get extend the known results (balanced, SKT, sG
manifolds), and are optimal in the compact case. Hence we can give new
non-trivial examples of generalized $p-$K\"ahler manifolds.
