Title: The Internal Dynamics of Ultra-Compact Dwarf Galaxies Abstract: Multi-object spectroscopic surveys of ultra-compact dwarf galaxies (UCDs) suggest that some of these objects have dynamical masses higher than predicted by canonical stellar population models based on the objects' luminosities. Possible scenarios for an extra, under-luminous mass component include dark matter, super-massive black holes, and variations of the stellar mass function leading to an overabundance of stellar remnants or of low-mass stars. In order to test these scenarois, we study in detail a small sample of UCDs, with considerable exposure times per target: Based on seeing limited observations obtained with the ARGUS Integral Field Unit (IFU) of the VLT/FLAMES spectrograph, we analyse the kinematics of UCD3, the brightest known UCD in the Fornax cluster and the first UCD with spatially resolved spectroscopy. The UCD's velocity dispersion profile is consistent with a model based on an isotropic velocity distribution and a constant mass to light ratio, which is consistent with that expected from stellar population models. No dark component is required to reproduce the shape of the profile. We obtained VLT/ISAAC spectroscopy in the K-band of two Virgo cluster UCDs, which have among the highest dynamical mass to light ratios of all known UCDs, in order to measure the 2.3$\mu$m CO-index, which can be used as a tracer for the abundance of low-mass stars in old stellar populations. As a reference for comparison, we observed extra-galactic globular clusters with similar metallicity. We find that one of the UCDs shows a significantly weaker CO-absorption than both, extra-galactic and Galactic globular clusters. This could indicate that the UCD exhibits a bottom-heavy stellar mass function.