  We give estimates on asymptotic dimensions of products of general hyperbolic
spaces with following applications to the hyperbolic groups. We give examples
of strict inequality in the product theorem for the asymptotic dimension in the
class of the hyperbolic groups; and examples of strict inequality in the
product theorem for the hyperbolic dimension. We prove that R is dimensionally
full for the asymptotic dimension in the class of the hyperbolic groups.
