Functional magnetic resonance imaging (fMRI) is a technique for studying the active human brain. During the fMRI experiment, a sequence of MR images is obtained, where the brain is represented as a set of voxels. The data obtained are a realization of a complex spatio-temporal process with many sources of variation, both biological and technical. Most current model-based methods of analysis are based on a two-step procedure. The initial step is a voxel-wise analysis of the temporal changes in the data while the spatial part of the modelling is done separately as a second step in the analysis. We present a spatio-temporal point process model approach for fMRI data where the temporal and spatial activation are modelled simultaneously. This modelling framework allows for more flexibility in the experimental design than most standard methods. It is also possible to analyze other characteristics of the data than just the locations of active brain regions, such as the interaction between the active regions. In this paper, we discuss statistical inference in the model based on mean value, variance and covariance. We analyze simulated data without repeated stimuli both for location of the activated regions and for interactions between the activated regions.