  The main part of the thesis deals with continuously and discretely
self-similar solutions and type II critical phenomena in a family of
self-gravitating non-linear sigma-models. The phenomena strongly depend on the
dimensionless coupling constant. For small couplings we numerically construct
continuously self-similar (CSS) solutions and analyze their stability
properties. For large couplings we construct a discretely self-similar (DSS)
solution with one unstable mode. We argue that at some critical coupling the
DSS solution bifurcates from the first CSS excitation in a heteroclinic loop
bifurcation. We study critical phenomena between dispersal and singularity
formation (at very small couplings) respectively black hole formation (for
larger couplings). We give numerical evidence that for very small couplings the
generic end state of ``intermediately strong'' data is the stable CSS ground
state. For small couplings the critical solution is the first CSS excitation
whereas for strong couplings the threshold of black hole formation is governed
by the DSS solution. We describe the phenomena occurring at intermediate
couplings where the critical solution changes from CSS to DSS.
  Content and references are at the state of October 2001.
