In this correspondence, we consider the maximum-likelihood (ML) direction-finding problem for wide-band sources. We examine the separable Gaussian and deterministic ML estimators, for several cases of a priori noise statistics. We derive general conditions under which the deterministic ML estimate is also an extremum of the Gaussian likelihood function. We also analyze the asymptotic performance of the wide-band ML estimators. We show that it is not affected by a priori knowledge of the noise spectrum, and formulate conditions under which the asymptotic performance of the deterministic and the Gaussian ML estimators are equal.