A recently developed synthetic technique, the polymerization in microemulsions, gives access to a new type of model polymer, spherical microgels or "rubbery nanospheres". These polymer molecules are narrowly distributed and have sizes in the range of 5 nm < R < 50 nm. In this paper, we report the examination of the viscoelastic behavior of these microgels in the bulk above their glass transition. Opposite to all expectations, these microgels show viscous flow up to molecular weights of M(W) = 2 x 10(6) or related hard-sphere radii of R = 9 nm, and the zero-shear viscosity is remarkably lower than the one of linear chains of the same molecular weight. Similarily surprising, it is shown that frequency dependence of the mechanical response looks like the well-known Zimm- or reptation-type response, although a Zimm- or reptation-like mobility can be strictly excluded by the spherical architecture of the molecules. These results support the existence of a strong, secondary type of polymer mobility besides reptation which is more cooperative in its nature than a single-chain mobility. This mobility should play an important role in all bulk polymer systems and might explain the rather high transport rates and deviations from reptation reported in many polymer systems with higher complexity.