Abstract. In the framework of supervised classification (discrimination) for functional data, it is shown that the optimal classification rule can be explicitly obtained for a class of Gaussian processes with ‘triangular’ covariance functions. This explicit knowledge has two practical consequences. First, the consistency of the well-known nearest neighbours classifier (which is not guaranteed in the problems with functional data) is established for the indicated class of processes. Second, and more important, parametric and non-parametric plug-in classifiers can be obtained by estimating the unknown elements in the optimal rule. The performance of these new plug-in classifiers is checked, with positive results, through a simulation study and a real data example.