Although recent fMRI studies on humor have begun to elucidate cognitive and affective neural correlates, they weren't able to distinguish between different logical mechanisms or steps of humor processing, i.e., the detection of an incongruity and its resolution. This fMRI study aimed to focus in more detail on cognitive humor processing. In order to investigate pure incongruity resolution without preprocessing steps, nonverbal cartoons differing in their logical mechanisms were contrasted with nonhumorous pictures containing an irresolvable incongruity. The logical mechanisms were: (1) visual puns (visual resemblance, PUNs); (2) semantic cartoons (pure semantic relationships, SEMs); and (3) Theory of Mind cartoons (which require additionally mentalizing abilities, TOMs). Thirty cartoons from each condition were presented to 17 healthy subjects while acquiring fMR images. The results reveal a left-sided network involved in pure incongruity resolution: e.g., temporo-parietal junction, inferior frontal gyrus and ventromedian prefrontal cortex. These areas are also involved in processing of SEMs, whereas PUNs show more activation in the extrastriate cortex and TOMs show more activation in so-called mentalizing areas. Processing of pictures containing an irresolvable incongruity evokes activation in the rostral cingulate zone, which might reflect error processing. We conclude that cognitive processing of different logical mechanisms depends on separate neural networks.