Abstract The Delayed-x LMS algorithm is a simplified version of the Filtered-x LMS algorithm, in which the modelC of the secondary pathCfrom the adaptive filter output to the error sensor is represented by a pure delay ofksamples (the delayed modelD) in order to reduce system complexity. However, the simplification produces a modelling error, which deteriorates the ANC performance. In this paper, the stability, especially that of the convergence characteristics of the feedforward active noise control system with the Delayed-x LMS algorithm, is investigated. It is shown that the stability is one in which the phase error (the phase difference between the secondary pathCand its delayed modelD) is in the range between −π/2 and π/2. Furthermore, it is shown that if the phase error is large, a small step-size parameter μ should be adopted to achieve stable noise cancellation, though the convergence speed becomes slow in the frequency domain. The theoretical results are verified by computer simulations.