In this paper, we develop a new implementation of maximum likelihood (ML) time delay estimation from direct-sequence CDMA (DS-CDMA) multipath transmissions. The formulation of the problem obtained from the DS-CDMA post-correlation model (PCM) leads to a non-linear likelihood function which is maximized by the iterative expectation maximization (EM) algorithm. In this approach, we avoid eigen-decomposition of the autocorrelation matrix widely used for multiple parameters estimation. Instead, we transpose the problem of multidimensional maximization to simpler one- dimensional maximizations carried out in parallel, thereby reducing the computational cost considerably. We also extend the application of the proposed single-carrier (SC) algorithm to multicarrier (MC)-CDMA systems by exploiting the frequency gain over subcarriers. Simulations suggest that the proposed EM-based algorithm provides accurate estimates even in the challenging case of closely-spaced delays from one transmitted symbol.