  We demonstrate the existence of non-abelian non-topological solitons such as
Q-balls in the spectrum of Wess-Zumino models with non-abelian global
symmetries. We conveniently name them Q-superballs and identify them for short
as Q-sballs. More specifically, we show that in contrast to the
non-supersymmetric case, they arise in renormalizable potentials with cubic
self-interactions of only one dimensionful parameter and for the entire
parameter space of the model available. We solve the field equations and
present the explicit form of the Q-sball solution. We compute its main physical
properties and observe that in the supersymmetrically invariant vacuum Q-sballs
form domains of manifestly broken sypersymmetry.
