In this paper, we describe a temporal model for event-related potentials (ERP) in the context of statistical parametric mapping (SPM). In brief, we project channel data onto a two-dimensional scalp surface or into three-dimensional brain space using some appropriate inverse solution. We then treat the spatiotemporal data in a mass-univariate fashion. This implicitly factorises the model into spatial and temporal components. The key contribution of this paper is the use of observation models that afford an explicit distinction between observation error and variation in the expression of ERPs. This distinction is created by employing a two-level hierarchical model, in which the first level models the ERP effects within-subject and trial type, while the second models differences in ERP expression among trial types and subjects. By bringing the analysis of ERP data into a classical hierarchical (i.e., mixed effects) framework, many apparently disparate approaches (e.g., conventional P300 analyses and time-frequency analyses of stimulus-locked oscillations) can be reconciled within the same estimation and inference procedure. Inference proceeds in the normal way using t or F statistics to test for effects that are localised in peristimulus time or in some time-frequency window. The use of F statistics is an important generalisation of classical approaches, because it allows one to test for effects that lie in a multidimensional subspace (i.e., of unknown but constrained form). We describe the analysis procedures, the underlying theory and compare its performance to established techniques.