Abstract. A general method to easily build global and relative operators for any number n of elementary systems if they are defined for 2 is presented. It is based on properties of the morphisms valued in the tensor products of algebras of the kinematics and it allows also the generalization to any n of relations demonstrated for two. The coalgebra structures play a peculiar role in the explicit constructions. Three examples are presented concerning the Galilei, Poincar and deformed Galilei algebras.