  We enlarge the class of $C^*$-algebras of Boolean dynamical systems in order
to include all weakly left-resolving normal labelled space $C^*$-algebras in
it. We prove a gauge-invariant uniqueness theorem and classify all
gauge-invariant ideals of these $C^*$-algebras of generalized Boolean dynamical
systems and describe the corresponding quotients as $C^*$-algebras of relative
generalized Boolean dynamical systems.
