  It is demonstrated how a many-body system far from thermal equilibrium can
exhibit universal dynamics in passing a non-thermal fixed point. As an example,
the process of Bose-Einstein (BE) condensation of a dilute cold gas is
considered. If the particle flux into the low-energy modes, induced, e.g., by a
cooling quench, is sufficiently strong, the Bose gas develops a characteristic
power-law single-particle spectrum $n(k)\sim k^{-5}$, and critical slowing down
in time occurs. The fixed point is shown to be marked by the creation and
dilution of tangled vortex lines. Alternatively, for a weak cooling quench and
particle flux, the condensation process runs quasi adiabatically, passing by
the fixed point in far distance, and signatures of critical scaling remain
absent.
