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This letter introduces a dynamic traffic grooming approach in bandwidth-flexible multi-layer IP/optical networks. A novel IP/optical multi-layer routing and grooming algorithm is proposed to calculate the routes for bitrate-flexible IP traffic over spectrum-flexible optical networks. The algorithm employs a bandwidth threshold, an auxiliary graph, and two grooming policies. Numerical results show that the dynamic grooming approach achieves lower blocking probabilities compared with IP-over-WDM and non-grooming flexible networks.