Summary: We study the inductive limit \(C^*\)-algebras associated with generalized Bratteli diagrams. For this purpose, we construct sequences of locally trivial \(C^*\)-bundles associated with their diagrams and study the inclusions of \(C^*\)-bundles. We give a complete condition to ensure locally trivial inclusions. Then we study generalized Bratteli diagrams arising from sequences of covering maps. We show that their inductive limit \(C^*\)-algebras come from lower semicontinuous cross sections of \(C^*\)-bundles. Using this, we prove that they are simple if the sequences of covering maps are minimal.