  We construct in a unifying way skew-multicategories and multicategories of
double and Gray-categories that we call Gray (skew) multicategories. We study
their different versions depending on the types of functors and higher
transforms. We construct Gray type products by generators and relations and
prove that Gray skew-multicategories are closed and representable on one side,
and that the Gray multicaticategories taken with the strict type of functors
are representable. We conclude that the categories of double and
Gray-categories with strict functors underlying Gray (skew) multicategories are
skew monoidal, respectively monoidal, depending on the type of the inner-hom
and product considered. The described Gray (skew) multicategories we see as
prototypes of general Gray (skew) multicategories, which correspond to (higher)
categories of higher dimensional internal and enriched categories.
