FL\(^2\)-algebras are lattice-ordered algebras with two sets of residuated operators. The classes RA of relation algebras and GBI of generalized bunched implication algebras are subvarieties of FL\(^2\)-algebras. We prove that the congruences of FL\(^2\)-algebras are determined by the congruence class of the respective identity elements, and we characterize the subsets that correspond to this congruence class. For involutive GBI-algebras the characterization simplifies to a form similar to relation algebras.