The optimal (by the criterion of maximum likelihood function) algorithm is applied to the problem of estimating the wave numbers of normal modes in an ocean waveguide. This algorithm has a high-resolution property, takes into account availability of correlated spatial noise, does not require prior modal decorrelation, is suitable for a horizontal array of any shape, and permits one to attain the potential wave-number estimation accuracy limit (Cramer–Rao bound). Numerical simulations for the Pekeris model of an ocean waveguide are presented, demonstrating that the optimal algorithm can essentially (more than ten times) improve the wave-number estimation performance relative to those one for the MUSIC algorithm. Wave-number estimation by the optimal algorithm requires searching for the global extremum of some goal function. It is connected, in common, with known computing difficulties and the absence of sufficiently well-developed computing algorithms. Algorithms based on the signal eigenvectors property of the spectral correlation matrix measured on the array elements are free from listed drawbacks. The synthesis of such algorithms and an asymptotic analysis of their performance are accomplished under conditions of arbitrary correlated spatial noise. Among these algorithms there is one that permits the estimation of the wave numbers as accurately as the optimal algorithm. Experimental verification of this result has been received for the most cases of practical interest.