  We study the classical and absolute stability of Q-balls in scalar field
theories with flat potentials arising in both gravity-mediated and
gauge-mediated models. We show that the associated Q-matter formed in
gravity-mediated potentials can be stable against decay into their own free
particles as long as the coupling constant of the nonrenormalisable term is
small, and that all of the possible three-dimensional Q-ball configurations are
classically stable against linear fluctuations. Three-dimensional
gauge-mediated Q-balls can be absolutely stable in the "thin-wall-like" limit,
but are completely unstable in the "thick-wall" limit.
