We report on measurements of relaxation times of nanometer-sized deformations resulting from the impact of individual energetic ions on poly͑methyl methacrylate͒ surfaces at temperatures close to and below the glass transition T g. The temporal evolution of the dimensions of the deformations is well described by a stretched exponential function, but with relaxation times ͑T͒ many orders of magnitude smaller than bulk values at the same T. The local T g was around 86°C, roughly 30°C below the conventional bulk T g. At the vicinity of the local T g , ͑T͒ follows the Vogel-Fulcher type of T dependence, but at lower T a transition towards a less steep behavior is seen.