Independent component analysis (ICA) is a promising analysis method that is being increasingly applied to fMRI data. A principal advantage of this approach is its applicability to cognitive paradigms for which detailed models of brain activity are not available. Independent component analysis has been successfully utilized to analyze single‐subject fMRI data sets, and an extension of this work would be to provide for group inferences. However, unlike univariate methods (e.g., regression analysis, Kolmogorov–Smirnov statistics), ICA does not naturally generalize to a method suitable for drawing inferences about groups of subjects. We introduce a novel approach for drawing group inferences using ICA of fMRI data, and present its application to a simple visual paradigm that alternately stimulates the left or right visual field. Our group ICA analysis revealed task‐related components in left and right visual cortex, a transiently task‐related component in bilateral occipital/parietal cortex, and a non‐task‐related component in bilateral visual association cortex. We address issues involved in the use of ICA as an fMRI analysis method such as: (1) How many components should be calculated? (2) How are these components to be combined across subjects? (3) How should the final results be thresholded and/or presented? We show that the methodology we present provides answers to these questions and lay out a process for making group inferences from fMRI data using independent component analysis. Hum. Brain Mapping 14:140–151, 2001. © 2001 Wiley‐Liss, Inc.