In this paper, we introduce the notion of Σ-hyperalgebras for an arbitrary signature Σ and provide some examples. Then we extend the notions of several kinds of homomorphisms and study their properties. Also, we study subhyperalgebras of a Σ-hyperalgebra A, Sub(A), under algebraic closure operators S, H and I. Finally, we introduce the notions of closed, invertible, ultraclosed and conjugable subhyperalgebras and investigate their connections to each other.