  A new kind of Q-balls is found: Q-balls in a non-linear sigma model. Their
main properties are presented together with those of their self-gravitating
generalization, sigma model Q-stars. A simple special limit of solutions which
are bound by gravity alone (``sigma stars'') is also discussed briefly. The
analysis is based on calculating the mass, global U(1) charge and binding
energy for families of solutions parameterized by the central value of the
scalar field. Two kinds (differing by the potential term) of the new sigma
model Q-balls and Q-stars are analyzed. They are found to share some
characteristics while differing in other respects like their properties for
weak central scalar fields which depend strongly on the form of the potential
term. They are also compared with their ``ordinary'' counterparts and although
similar in some respects, significant differences are found like the existence
of an upper bound on the central scalar field. The sigma model Q-stars also
contain non-solitonic solutions whose relation with sigma star solutions is
discussed.
