  We present for the first time solutions in the gauged $U(1)\times U(1)$ model
of Witten describing vortons -- spinning flux loops stabilized against
contraction by the centrifugal force. Vortons were heuristically described many
years ago, however, the corresponding field theory solutions were not obtained
and so the stability issue remained open. We construct explicitly a family of
stationary vortons characterized by their charge and angular momentum. Most of
them are unstable and break in pieces when perturbed. However, thick vortons
with small radius preserve their form in the 3+1 non-linear dynamical
evolution. This gives the first ever evidence of stable vortons and impacts
several branches of physics where they could potentially exist. These range
from cosmology, since vortons could perhaps contribute to dark matter, to QCD
and condensed matter physics.
