Viscosities of 18 North Sea oils (API gravity 23.8 to 47.6) have been measured at temperatures between 40 and 0 degrees C and shear rates ranging from 30 to 500 s(-1). Precipitated wax has a pronounced effect on the viscosity and rheological behavior of these oils. At low temperatures where wax precipitation is most extensive, the oils typically behave like pseudoplastic or viscoplastic fluids. A shear-rate-dependent viscosity model is presented. It is based on a correspondence between viscosity and volume fraction of precipitated wax and further uses the Casson rheological fluid model. It contains a Newtonian and two shear-rate-dependent terms. The Newtonian term is similar to the type of viscosity models used for oil/water emulsions. The model correlates 713 measured viscosity data points with an average absolute deviation of 48%. The model has been tested on three oils not included in the data basis. The non-Newtonian viscosities of these oils (176 data points) were predicted with an average absolute deviation of 47%.