The low energy muon (LEM) technique has been used to probe local changes in the dynamical spectrum of thin film polymer samples taking place as a function of the temperature and the implantation depth below the free surface. The studies have been made on samples of polydimethylsiloxane (PDMS) and polybutadiene (PB) using the transverse magnetic field (TF) configuration and diamagnetic probe muons. In PDMS evidence is found for suppression of the glass transition temperature near the surface, along with significantly modified dynamics in the near-surface region as well as at depths significantly below the surface. For PB the LEM technique reveals well-defined layers of dynamical and spatial in homogeneity at depths of order 0.1-0.2 mu m below the free surface. These inhomogeneous regions may be assigned to nanopores produced by solvent streaming during preparation of spin-cast films. A thermal annealing procedure is shown to significantly reduce the thickness of these inhomogeneous layers. These results demonstrate that using LEM in the TF configuration provides a promising new method for studying surface-modified local dynamics of polymers that is also able to reveal nanostructured buried layers in polymer films. (C) 2016 Published by Elsevier Ltd.