A random field model is developed for the occurrence of earthquakes in the space-time domain based on the theory of random functions. The seismic hazard posed by earthquakes is estimated by applying the level crossing theory to local integral random functions. Analysis of the correlation structure of the strain energy random field associated with the proposed model is described by utilizing the concepts of variance function and scale of fluctuation. The earthquake occurrence rates obtained in the study differ from the classical earthquake occurrence rates in the sense that these rates are adjusted for the degree of correlation in space and time. The theory and the results of the study are applied to a real-life problem involving the assessment of seismic hazard for the North Anatolian Fault Zone (NAFZ). The annual seismic hazard obtained from the random field model developed in this study is found to be consistent with the observed seismic activity along the NAFZ. (C) 2000 Elsevier Science B.V. All rights reserved.