In this paper poly-algebras of a given type $\mathcal F$ are considered. Namely, $\emptyset\neq\mathcal F=\cup\{\mathcal F_n:n\geq0\}$ is a disjoint union, and a poly-$\mathcal F$-algebra $\mathcal A$ with a carrier $A\neq\emptyset$ is a mapping $\mathcal A\colon f\to f^{\mathcal A}$ such that $f^{\mathcal A}\colon A^n\to\mathcal P(A)$, for every $f\in\mathcal F_n$, $n\geq0$. Subalgebras are defined in the usual way, but, there are considered three kinds of homomorphisms, which implies three kinds of "freeness". Several results about subalgebras, homomorphisms and free objects in different classes of poly-algebras are given.