We investigate both theoreticaally and experimentally the nonlinear propagation of surface plasmon polaritons (SPP) on a single air/metal interface. Inspired by nonlinear dielectric waveguide theory, we analytically derive a model that describes the nonlinear propagation of SPPs, thus bridging the description of plasmonic and dielectric waveguides. The model, the numerical simulations and the experiments, which are carried out in the hundred femtosecond regime, reveal that the SPP undergoes strong ultrafast self-action which manifests itself through selfinduced absorption. Our observations are consistent with a large, bulk, third-order nonlinear susceptibility (χ(3)) of gold and provide a selfconsistent theory of self-action of SPPs at an air/metal interface. Experimentally, we find Im{χ (3)} 3×10-16 m2/V2. These findings have important implications in the nonlinear physics of plasmonics and metamaterials as they provide evidence that nonlinear absorption has a significant effect on the propagation of SPPs excited by intense optical pulses. This self-action is also expected to affect the anomalous absorption of light near subwavelength structures as well as the strength of desirable nonlinear processes such as third-harmonic generation and four-wave mixing, which will inevitably compete with nonlinear absorption.