We propose a novel approach for space-time functional data analysis based on aspace-time autoregressive Hilbertian model. This model can capture the dynamicand spatial dependence of functional data over time and space. We provide suf-ficient conditions for the existence and uniqueness of the model and establish itsasymptotic properties, such as the strong law of large numbers and the centrallimit theorem. We also develop a consistent estimator for the model parametersand evaluate its performance through simulations and a real data example onwind speed data.