This chapter introduces and explores Nn-algebras as the algebraic structures corresponding to the family of non-alethic logics—a symbiosis of paraconsistent and paracomplete logical systems. Originating from the analysis of the Cn and Pn calculi, the Nn systems reject both the Principle of Non-contradiction and the Principle of Excluded Middle, enabling formal reasoning in contexts of inconsistency and indeterminacy. The chapter systematically defines the Nn logical calculi, their algebraic semantics, and structural properties, culminating in the formalization of Curry Nn-algebras and propositional Nn-algebras. Representation theorems are established, showing that each Nn-algebra corresponds to a Boolean algebra of clopen sets in totally disconnected compact Hausdorff spaces. The hierarchical relationship among Nn, Cn, Pn, and Boolean algebras is made explicit, demonstrating how classical, paraconsistent, and paracomplete systems emerge as particular cases. The framework offers significant implications for formal logic, particularly in fields like artificial intelligence and systems reasoning under uncertainty.