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Many neurological diseases are characterized by gradual deterioration of brain structure and function. Large longitudinal MRI datasets have revealed such deterioration, in part, by applying machine and deep learning to predict diagnosis. A popular approach is to apply Convolutional Neural Networks (CNN) to extract informative features from each visit of the longitudinal MRI and then use those features to classify each visit via Recurrent Neural Networks (RNNs). Such modeling neglects the progressive nature of the disease, which may result in clinically implausible classifications across visits. To avoid this issue, we propose to combine features across visits by coupling feature extraction with a novel longitudinal pooling layer and enforce consistency of the classification across visits in line with disease progression. We evaluate the proposed method on the longitudinal structural MRIs from three neuroimaging datasets: Alzheimer's Disease Neuroimaging Initiative (ADNI, N=404), a dataset composed of 274 normal controls and 329 patients with Alcohol Use Disorder (AUD), and 255 youths from the National Consortium on Alcohol and NeuroDevelopment in Adolescence (NCANDA). In all three experiments our method is superior to other widely used approaches for longitudinal classification thus making a unique contribution towards more accurate tracking of the impact of conditions on the brain. The code is available at https://github.com/ouyangjiahong/longitudinal-pooling.