  The property of a normal functor to be open-multicommutative proposed by
Kozhan and Zarichnyi (2004) is investigated. A number of normal functors
related to the functor of probability measures and equipped with convex
structure are considered here and it is proved that the functors $cc$, $ccP$,
$G_{cc}P$ and $\lambda_{cc}P$ are open-multicommutative.}
