Atomic force microscopy is used to investigate the dynamic viscoelastic response of a low-molecular-weight polymer liquid, poly(dimethylsiloxane) (PDMS), constrained between a flat silicon wafer and a tip made from a glass sphere, Capillary forces dominate the response at low frequency, and viscous forces dominate at high frequency. The magnitude of the capillary interaction between the AFM til, and the polymer liquid is determined by the thickness af PDMS deposited onto the silicon wafer. The frequency spectrum can be effectively described by a simple mechanical model that assumes the polymer film responds as a Newtonian liquid, The model demonstrates that viscous forces can lead Co a predominantly in-phase response due to the compliance of the AFM cantilever, Measurements of the viscous damping coefficient as a function of the separation between the tip and the substrate allow a quantitative determination of the viscosity of the polymer constrained between the two surfaces; this value for viscosity agrees well with the bulk viscosity for separations greater than about 25 nm, For smaller separations, the microroughness of the glass spheres used as tips prevents an accurate determination of the viscosity.