The concept of a relational hypersubstitution for algebraic systems of type is an extension of the concept of a hypersubstitution for universal algebra of type τ. The set of all relational hypersubstitutions for algebraic systems of type together with a binary operation forms a monoid. In this paper, we study the semigroup properties of the monoid of type ((m), (n)) for arbitrary natural numbers  In particular, we characterize all idempotent elements and all regular elements of this monoid.

hypersubstitution, relational hypersubstitution, algebraic systems, idempotent elements, regular elements.