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Single-subject mapping of resting-state brain functional activity to non-imaging phenotypes is a major goal of neuroimaging. The large majority of learning approaches applied today rely either on static representations or on short-term temporal correlations. This is at odds with the nature of brain activity which is dynamic and exhibit both short- and long-range dependencies. Further, new sophisticated deep learning approaches have been developed and validated on single tasks/datasets. The application of these models for the study of a different targets typically require exhaustive hyperparameter search, model engineering and trial and error to obtain competitive results with simpler linear models. This in turn limit their adoption and hinder fair benchmarking in a rapidly developing area of research. To this end, we propose fMRI-S4; a versatile deep learning model for the classification of phenotypes and psychiatric disorders from the timecourses of resting-state functional magnetic resonance imaging scans. fMRI-S4 capture short- and long- range temporal dependencies in the signal using 1D convolutions and the recently introduced state-space models S4. The proposed architecture is lightweight, sample-efficient and robust across tasks/datasets. We validate fMRI-S4 on the tasks of diagnosing major depressive disorder (MDD), autism spectrum disorder (ASD) and sex classifcation on three multi-site rs-fMRI datasets. We show that fMRI-S4 can outperform existing methods on all three tasks and can be trained as a plug&play model without special hyperpararameter tuning for each setting