We develop several kernel methods for classification of longitudinal data and apply them to detect cognitive decline in the elderly. We first develop mixed-effects models, a type of hierarchical empirical Bayes generative models, for the time series. After demonstrating their utility in likelihood ratio classifiers (and the improvement over standard regression models for such classifiers), we develop novel Fisher kernels based on mixture of mixed-effects models and use them in support vector machine classifiers. The hierarchical generative model allows us to handle variations in sequence length and sampling interval gracefully. We also give nonparametric kernels not based on generative models, but rather on the reproducing kernel Hilbert space. We apply the methods to detecting cognitive decline from longitudinal clinical data on motor and neuropsychological tests. The likelihood ratio classifiers based on the neuropsychological tests perform better than than classifiers based on the motor behavior. Discriminant classifiers performed better than likelihood ratio classifiers for the motor behavior tests.