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For a train composed of a number of identical cars moving over a bridge at high speeds, train-induced resonance may occur on the bridge when any frequency of the bridge coincides with any of those implied by the wheel loads.Similarly, for a vehicle moving over a series of bridges with identical spans at constant speeds,bridge-induced resonance may occur on the vehicle when any frequency of the vehicle coincides with any of the bridges.The most general case occurs when a train composed a number of carriages moving over a series of simple beams.The analyses indicate that train-induced resonance on the bridges takes place at higher speeds, but bridge-induced resonance on the train cars at lower speeds.