The principles and theoretical background are presented for a new process-based model (PESERA) that is designed to estimate long-term average erosion rates at 1 km resolution and has, to date, been applied to most of Europe. The model is built around a partition of precipitation into components for overland flow (infiltration excess, saturation excess and snowmelt), evapo-transpiration and changes in soil moisture storage. Transpiration is used to drive a generic plant growth model for biomass, constrained as necessary by land use decisions, primarily on a monthly time step. Leaf fall, with corrections for cropping, grazing, etc., also drives a simple model for soil organic matter. The runoff threshold for infiltration excess overland flow depends dynamically on vegetation cover, organic matter and soil properties, varying over the year. The distribution of daily rainfall totals has been fitted to a Gamma distribution for each month, and drives overland flow and sediment transport (proportional to the sum of overland flow squared) by summing over this distribution. Total erosion is driven by erodibility, derived from soil properties, squared overland flow discharge and gradient; it is assessed at the slope base to estimate total loss from the land, and delivered to stream channels.