Encoding models are used for predicting brain activity in response to sensory stimuli with the objective of elucidating how sensory information is represented in the brain. Encoding models typically comprise a nonlinear transformation of stimuli to features (feature model) and a linear transformation of features to responses (response model). While there has been extensive work on developing better feature models, the work on developing better response models has been rather limited. Here, we investigate the extent to which recurrent neural network models can use their internal memories for nonlinear processing of arbitrary feature sequences to predict feature-evoked response sequences as measured by functional magnetic resonance imaging. We show that the proposed recurrent neural network models can significantly outperform established response models by accurately estimating long-term dependencies that drive hemodynamic responses. The results open a new window into modeling the dynamics of brain activity in response to sensory stimuli.