This paper presents experiments on run-up of strongly nonlinear waves on a beach of 10.54° inclination. Velocity fields are obtained by the PIV (particle image velocimetry) technique. Acceleration measurements are also attempted, but it is difficult to obtain useful results in every case. In addition, free-surface profiles are extracted from digital images and wave resistance probes. The investigation focuses on the dynamics of the early stages of the run-up, when steep fronts evolve in the vicinity of the equilibrium shoreline, but maximum run-up heights are also reported. Measurements on moderately nonlinear waves are compared to results from long-wave theories, including a numerical Boussinesq model and analytic shallow-water results from the literature. In particular the applicability of the long-wave theories is addressed. However, most attention is given to run-up of high incident solitary waves that are on the brink of breaking at the shoreline. In one case a temporarily slightly overturning wave front is found that neither develops into a plunger or displays appreciable spilling. This feature is discussed in view of measured velocity and acceleration patterns and with reference to the dam-break problem. Effects of scaling, as well as viscous damping, are also briefly discussed.