The profile of a liquid front of a polymer film dewetting a solid substrate is examined by atomic force microscopy. The material removed from the substrate is accumulated in a rim next to the three-phase contact line. Theory predicts the leading edge of the rim profile to be a damped harmonic oscillation for a large class of systems. This is investigated experimentally for the first time, and we show that a non-Newtonian liquid behaves qualitatively different due to viscoelastic effects. It is pointed out that analysis of the rim shapes allows one to study quantitatively the rheological properties of complex fluids on a nanometer scale.