  We report on a new behavior found in numerical simulations of spherically
symmetric gravitational collapse in self-gravitating SU(2) sigma models at
intermediate gravitational coupling constants: The critical solution (between
black hole formation and dispersion) closely approximates the continuously
self-similar (CSS) solution for a finite time interval, then departs from this,
and then returns to CSS again. This cycle repeats several times, each with a
different CSS accumulation point. We have preliminary evidence that this same
critical solution is also discretely self-similar (DSS) between the CSS
episodes, but with an echoing period $\Delta$ which varies during the
evolution.
