Under-deck cable-stayed bridges are innovative bridge configurations in which stays are located underneath the deck. This bridge typology can lead to highly efficient and slender decks, resulting in a large reduction of the amount of materials employed. Nevertheless, if very slender decks are designed, vibration problems can arise potentially compromising the comfort of bridge users. The dynamic response of an under-deck cable-stayed bridge with a steel-concrete composite deck under the action of moving loads is studied. After an initial modal analysis, the contribution of each mode is identified. Loads applied eccentrically on the cross-section of the deck are found to increase accelerations substantially. Amplification and cancellation speeds are observed to govern the maximum accelerations registered on the deck. A parametric analysis reveals the maximum slendernesses that can be achieved to satisfy different comfort criteria.