This paper presents the theoretical work about active noise cancellation in ducts. The proposed control system is designed based on the assumption of a one-dimensional sound field. The controller consists of a feedforward block which serves as a noise observer. The feedback portion of the control algorithm is to minimize residual disturbances. Closed-loop stability of the MIMO (multiple-input-multiple-output) system is analyzed and the result shows that the dynamic influenced by the space-feedforward and feedback controllers can be decoupled. Both semi-infinite and finite-length ducts are considered in this study and simulation examples are given to illustrate the effectiveness of the proposed controllers.