Algebraic systems play in the theory of algebraizability of π-institutions the role that algebras play in the theory of algebraizable sentential logics. In this same sense, ℐ-algebraic systems are to a π-institution ℐ what S\mathcal{S} -algebras are to a sentential logic S\mathcal{S} . More precisely, an (ℐ,N)-algebraic system is the sentence functor reduct of an N′-reduced (N,N′)-full model of a π-institution ℐ. Algebraic systems are formally introduced and their relationship with full models and with bilogical morphisms is investigated.