Discrimination problems in a high-dimensional setting are considered. New results are concerned with the role of dimensionality in the performance of the discrimination procedure. Assuming that data consist of a block structurc two different asymptotic approaches are presented. These approaches are characterized by different types of relations between the dimensionality and the size of the training samples.par Asymptotic expressions for the error probabilities are obtained and a consistent approximation of the discriminant function is proposed. Throughout the paper the importance of the dimensionality in the asymptotic analysis is stressed.