In this paper we consider two kinds of free structures: "free" and "strongly free" poly-algebras. We shall give a complete description of free objects over the class of regular poly-algebras and show the existence of strongly free object in the class of $\alpha$-bounded regular objects, where $\alpha$ is a non-empty cardinal. If a is finite, two strongly free objects with the same basis are isomorphic, and in this case we have a complete description of strongly free objects. But, if a is infinite, then there exist non-isomorphic strongly free objects with the same basis.