Abstract We introduce a generalization of L-algebras motivated by investigations into the structure of quantum logic, termed quasi-L-algebras. After establishing the foundational structure theory for such quasi-L-algebras, we delve into the class of quasi-L-algebras, denoted as $$\mathcal{Q}\mathcal{L}$$ Q L , which forms a quasivariety. Utilizing the fact that every quasi-L-algebra can be embedded into the direct product of an L-algebra and a flat quasi-L-algebra, we determine a generator for $$\mathcal{Q}\mathcal{L}$$ Q L . Lastly, we explore congruence relations on a quasi-L-algebra L and their connections with ideals and weak ideals of L, as well as the ideals of the L-algebra R(L). We also propose a representation for congruence relations on each quasi-L-algebras.