The active control of broadband noise in duct systems has achieved enormous success in the past two decades. However, the performance of such an active noise control (ANC) system is limited by the presence of higher order duct modes. To alleviate this limitation of such an ANC system requires the development of a multi-modal control system. This dissertation compares the performance of two multi-modal control strategies in a duct system and also compares two adaptive filter algorithms, i.e. the filtered-x LMS and filtered-u RLMS algorithms. It was found that the choice of adaptive filter algorithms for a multi-modal ANC in a duct system is less important than the overall control strategy. Also, the performance of such a multi-modal ANC system can be misleading if it is not evaluated at a set of monitoring sensor locations which are further downstream than the error sensors used by the adaptive algorithm. It was also found that the performance of an ANC system will be degraded when the acoustic waves in the duct and the wall displacement are strongly coupled together. Consequently, this multi-modal ANC system is operated and measured in a circular duct system where the acoustic and vibration coupling problem can be avoided. However, the corresponding controller performance was affected by the 'modal sensitivity' and 'modal cross-coupling effect' in a circular duct system.