  We consider inverse curvature flows in the $(n+1)$-dimensional Euclidean
space, $n\geq 2,$ expanding by arbitrary negative powers of a 1-homogeneous,
monotone curvature function $F$ with some concavity properties. We obtain
asymptotical roundness, meaning that circumradius minus inradius of the flow
hypersurfaces decays to zero and that the flow becomes close to a flow of
spheres.
