In active noise control where a delay in an error path is necessary or Unaboidable, the algorithm is customarily used in the Delayed Least Mean Square (DLMS) form. In this thesis, we study the behavior of the DLMS algorithm with the use of computer simulation to determine its convergence and stability properties. It is noted that the presence of the delay in the error path requires that the convergence factor be relatively small to avoid instability, which therefore slows down the convergence rate. We then propose a new alternative of the DLMS algorithm to avoid the drawbacks. The proposed algorithm is formulated using an error adjustment procedure. The convergence behavior of the new algorithm is similar to that of the standard least mean square (LMS) algorithm. Further refinement using a power of two quantizing method then reduces the number of multiplications and divisions per input sample (MADPS) without changing the convergence behavior significantly. The ideas behind proposed algorithm and its simplified version are also applicable to the normalized DLMS (NDLMS) algorithm.