A b s t r a c t. We discuss quasivarieties related in some special sense to sequent calculi. We show that the free algebra in such a \qv\ is Fregean iff the sequent calculus has so-called {\it symmetric contraction} rules admissible. In the presence of the fusion connective this is equivalent to having contraction. With every sequent calculus $\cG$ one can associate, in some way, a sequent calculus with fusion. If this calculus has a separability property then a quasivariety $\Q$ related to $\cG$ is the class of fusion-less reducts of some quasivariety of algebras with fusion.