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We consider the problem of maximum-likelihood (ML) direction-of-arrival (DOA) estimation of underwater acoustic signals from ships, submarines, or torpedoes, which contain both sinusoidal and random components, and are called mixed signals in this paper. We model the mixed signals as the mixture of deterministic sinusoidal signals and stochastic Gaussian signals, and derive the ML DOA estimator for the mixed signals under spatially white noise. We compute the asymptotic error covariance matrix of the proposed ML estimator, as well as that of the typical stochastic estimator assuming zero-mean Gaussian signals, for DOA estimation of mixed signals. Our analytical comparison and numerical examples show that the proposed ML estimator, which takes advantage of the sinusoidal components in the mixed signals, improves the DOA estimation accuracy for the mixed signals compared with the typical stochastic estimator assuming zero-mean Gaussian signals.