 There are selfextensional and non-selfextensional logics in any one of the classes of the Leibniz hierarchy and also in the class of non-protoalgebraic logics. These facts show that the perspective that leads to the consideration of the classes in the Leibniz hierarchy and the perspective that leads to the definition of the selfextensional and the Fregean logics as classes of logics worthy of study as a whole are to a large extent different. Nonetheless, one of the trends of today’s research in abstract algebraic logic is to determine the interplay between the two perspectives and study the classes of logics that arise when crossing both classifications. In fact, there is a connection between the replacement principles and the Suszko congruence (and thus with the Leibniz congruence). A logic \(\bL\) satisfies the strong replacement principle if and only if for every \(\bL\)-theory \(T\) its Suszko congruence is the interderivability relation relative to \(T\), namely the relation \(\{\langle \phi , \psi \rangle : T, \phi \vdash_{\bL } \psi\) and \(T, \psi \vdash_{\bL } \phi \}\). And a logic \(\bL\) satisfies the weak replacement principle if and only if the Suszko congruence of the set of theorems of \(\bL\) is the interderivability relation \(\{\langle \phi , \psi \rangle : \phi \vdash_{\bL } \psi\) and \(\psi \vdash_{\bL } \phi \}\).