The problem of waveband switching (WBS) in a wavelength-division multiplexing (WDM) mesh network with dynamic traffic requests is investigated. To solve the WBS problem in a homogeneous dynamic WBS network, where every node is a multigranular optical crossconnect (MG-OXC), we construct an auxiliary graph. Based on the auxiliary graph, we develop two heuristic on-line WBS algorithms with different grouping policies, namely the wavelength-first WBS algorithm based on the auxiliary graph (WFAUG) and the waveband-first WBS algorithm based on the auxiliary graph (BFAUG). Our results show that the WFAUG algorithm outperforms the BFAUG algorithm.