In this paper we consider hyperalgebras and hyper-coalgebras of type Ą ,
as an analogue of algebras of type Ą and coalgebras of type Ą (see [10]). Hyperalgebras
and hyper-coalgebras are special cases of (F1, F2)-systems. Therefore many of the
results in this paper will be instances of (F1, F2)-system results (see [8]). Nevertheless
it is interesting and instructive to consider directly the theory of hyperalgebras and
hyper-coalgebras of type Ą . The aim of this paper is to create a unified theory of
hyperalgebras and hyper-coalgebras which is based on (F1, F2)-systems.