Many of the adaptive noise control systems utilize a form of the least mean square (LMS) algorithms. In the active control of noise, it is common practice to locate an error microphone far from the control source to avoid the near-field effects by evanescent waves. Such a distance between the control source and the error microphone makes a certain level of time-delay inevitable and, hence, may yield undesirable effects on the convergence properties of control algorithms such as filtered-x LMS. This paper discusses the dependence of the convergence rate on the acoustic error path in these popularalgorithms and introduces new algorithms which increase the convergence region regardless of the time-delay in the acoustic error path. Performances of the new LMS algorithms are presented in comparison with those by the conventional algorithms based on computer simulations and experiments.