Automatic eye localization is a crucial part of many computer vision algorithms for processing face images. Some of the existing algorithms can be very accurate, albeit at the cost of computational complexity. In this paper, a new solution to the problem of automatic eye localization is proposed. Eye localization is posed as a nonlinear regression problem solved by two feed-forward multilayer perceptrons (MLP) working in a cascade. The input feature vector of the first network is constructed from coefficients of a two dimensional discrete cosine transform(DCT) of a face image. The second network generates corrections based on small image patches. Feature extraction and neural network prediction have known and efficient implementations, thus the entire procedure can be very fast. The paper hints at the neural network structure and the procedure for generating artificial training samples from a low number of face images. In terms of accuracy, the method is comparable to state-of-the-art techniques; however it is based on numerical procedures that could be highly optimized (fast Fourier transform and matrix multiplication).