We consider the estimation of channel parameters for code division multiple access (CDMA) communication systems operating over channels with either single or multiple propagation paths. We present two approaches for decomposing this multiuser channel estimation problem into a series of single user problems. In the first method, the interfering users are treated as colored, non-Gaussian noise, and the maximum likelihood estimate is formed from the sample mean and sample covariance matrix of the received signal. In the second method, we exploit the eigenstructure of the sample correlation matrix to partition the observation space into a signal subspace and a noise subspace. The channel estimate is formed by projecting a given user's spreading waveform into the estimated noise subspace and then either maximizing the likelihood or minimizing the Euclidean norm of this projection. Both of these approaches yield algorithms which are near-far resistant and are capable of tracking slowly varying channels.