Parametric statistical methods, such as Z-, t-, and F-values, are traditionally employed in functional magnetic resonance imaging (fMRI) for identifying areas in the brain that are active with a certain degree of statistical significance. These parametric methods, however, have two major drawbacks. First, it is assumed that the observed data are Gaussian distributed and independent; assumptions that generally are not valid for fMRI data. Second, the statistical test distribution can be derived theoretically only for very simple linear detection statistics. With nonparametric statistical methods, the two limitations described above can be overcome. The major drawback of non-parametric methods is the computational burden with processing times ranging from hours to days, which so far have made them impractical for routine use in single-subject fMRI analysis. In this work, it is shown how the computational power of cost-efficient graphics processing units (GPUs) can be used to speed up random permutation tests. A test with 10000 permutations takes less than a minute, making statistical analysis of advanced detection methods in fMRI practically feasible. To exemplify the permutation-based approach, brain activity maps generated by the general linear model (GLM) and canonical correlation analysis (CCA) are compared at the same significance level.