This paper describes application of Support Vector Machines (SVM) methodology for fMRI activation detection. Whereas SVM methods have been successfully used for standard predictive learning settings (i.e., classification and regression), the goal of activation detection, strictly speaking, is not achieving improved prediction accuracy. We relate the problem of activation detection in fMRI to the problem feature selection in machine learning, and describe various multivariate supervised-learning formulations for this application. Due to extreme ill-posedness of typical fMRI data sets, the quality of activation detection will be greatly affected by (a) incorporating a priori knowledge into SVM formulations, and (b) using proper encoding for training data. We analyze these issues separately, and introduce (a) novel spatial SVM formulation (reflecting a priori knowledge about local spatial correlations in fMRI data) and (b) two new encoding schemes for fMRI data that incorporate the effects of the brain dynamics (i.e., its Hemodynamic Response Function, or HRF). The effectiveness of these modifications is clearly demonstrated using benchmark simulated and real-life fMRI data sets.