Controlling the annular frictional pressure losses is important in order to drill safely with overpressure without fracturing the formation. To predict these pressure losses, however, is not straightforward. First of all, the pressure losses depend on the annulus eccentricity. Moving the drillstring to the wall generates a wider flow channel in part of the annulus which reduces the frictional pressure losses significantly. The drillstring motion itself also affects the pressure loss significantly. The drillstring rotation, even for fairly small rotation rates, creates unstable flow and sometimes turbulence in the annulus even without axial flow. Transversal motion of the drillstring creates vortices that destabilize the flow. Consequently, the annular frictional pressure loss is increased even though the drilling fluid becomes thinner because of added shear rate. Naturally, the rheological properties of the drilling fluid play an important role. These rheological properties include more properties than the viscosity as measured by API procedures. It is impossible to use the same frictional pressure loss model for water based and oil based drilling fluids even if their viscosity profile is equal because of the different ways these fluids build viscosity. Water based drilling fluids are normally constructed as a polymer solution while the oil based are combinations of emulsions and dispersions. Furthermore, within both water based and oil based drilling fluids there are functional differences. These differences may be sufficiently large to require different models for two water based drilling fluids built with different types of polymers. In addition to these phenomena washouts and tool joints will create localised pressure losses. These localised pressure losses will again be coupled with the rheological properties of the drilling fluids. In this paper, all the above mentioned phenomena and their consequences for annular pressure losses will be discussed in detail. North Sea field data is used as an example. It is not straightforward to build general annular pressure loss models. This argument is based on flow stability analysis and the consequences of using drilling fluids with different rheological properties. These different rheological properties include shear dependent viscosity, elongational viscosity and other viscoelastic properties.