We have investigated the surface mobility of thin films (<5 nm thick)of linear chain perfluoropolyether polymers on silicon and CN@sub x@ surfaces while subjecting them to air shear stresses. These experiments are elucidating the nature of viscosity in molecularly thin films of lubricants important for magnetic recording. For polymer chains with neutral CF@sub 3@ end groups, we find that the effective viscosity is close to the bulk viscosity even at sub-monolayer coverage. The addition of alcohol end groups to the polymer chains acts to anchor the first layer of molecules to a surface, greatly increasing the effective viscosity relative to the bulk. For the second layer, the alcohol-terminated polymers exhibit effective viscosities near their bulk viscosity, while dewetting is observed in thicker films.