Velocity lag between the two discs in the eccentric disc rheometer is determined analytically for a Newtonian fluid, the second order fluid, and for general simple fluids when the offset and slip are small. It is established that the normal thrust between the discs does not measure the second normal stress difference. Experimental measurements of the velocity lag are in good agreement with the analytical expressions which are developed. The influence of the velocity lag on the forces exerted on the free disc is predicted. Experimental results with two different edge geometries indicate the strong influence of edge effects on the forces exerted on the free disc. The correct relationship between the fluid viscosity and the measured forces, therefore, may require detailed analysis of the flow situation in the edge region or careful experimental extrapolation procedures.