We aimed to study the neural processing of emotion-denoting words based on a circumplex model of affect, which posits that all emotions can be described as a linear combination of two neurophysiological dimensions, valence and arousal. Based on the circumplex model, we predicted a linear relationship between neural activity and incremental changes in these two affective dimensions. Using functional magnetic resonance imaging, we assessed in 10 subjects the correlations of BOLD (blood oxygen level dependent) signal with ratings of valence and arousal during the presentation of emotion-denoting words. Valence ratings correlated positively with neural activity in the left insular cortex and inversely with neural activity in the right dorsolateral prefrontal and precuneus cortices. The absolute value of valence ratings (reflecting the positive and negative extremes of valence) correlated positively with neural activity in the left dorsolateral and medial prefrontal cortex (PFC), dorsal anterior cingulate cortex, posterior cingulate cortex, and right dorsal PFC, and inversely with neural activity in the left medial temporal cortex and right amygdala. Arousal ratings and neural activity correlated positively in the left parahippocampus and dorsal anterior cingulate cortex, and inversely in the left dorsolateral PFC and dorsal cerebellum. We found evidence for two neural networks subserving the affective dimensions of valence and arousal. These findings clarify inconsistencies from prior imaging studies of affect by suggesting that two underlying neurophysiological systems, valence and arousal, may subserve the processing of affective stimuli, consistent with the circumplex model of affect.