As part of a multi-epoch and multi-wavelength study of the physics of core dominated radio sources we have investigated the occurrence of apparent superluminal motion and other indications for bulk relativistic motion (b.r.m) in a statistically complete, flux density limited (S5GHz ≥ 1Jy) sample of 13 objects with flat radio spectra These sources come from the S5-survey (Kühr et al., 1981) and are optically identified as 7 quasars and 6 BL-Lac objects. They have been observed over a wide range of frequencies, from radio through X-rays (s. Eckart et al., 1986 and references therein). Radiomaps have been obtained at frequencies from 327 MHz to 22.2 GHz with resolutions from arcseconds to 0.2 mas, using the VLA, MERLIN and telescopes of the US- and European-VLBI networks. A recent status report on the VLBI-observations is given by Witzel (1987). In this paper we summarize the results on the direct evidence for b.r.m. in this sample as derived from repeated VLBI-observations at 5 GHz, as well as supporting evidence from SSC-calculations and flux density variability of the 5GHz VLBI core components (Table 1).