We present maximum likelihood (ML) methods for estimating evoked dipole responses using electroencephalography (EEG) and magnetoencephalography (MEG) arrays, which allow for spatially correlated noise between sensors with unknown covariance. The electric source is modeled as a collection of current dipoles at fixed locations and the head as a spherical conductor. We permit the dipoles' moments to vary with time by modeling them as linear combinations of parametric or nonparametric basis functions. We estimate the dipoles' locations and moments and derive the Cramer-Rao bound for the unknown parameters. We also propose an ML based method for scanning the brain response data, which can be used to initialize the multidimensional search required to obtain the true dipole location estimates. Numerical simulations demonstrate the performance of the proposed methods