  The Einstein-Yang-Mills equations are the source of many interesting
solutions within general relativity, including families of particle-like and
black hole solutions, and critical phenomena of more than one type. These
solutions, discovered in the last thirty years, all assume a restricted form
for the Yang-Mills gauge potential known as the "magnetic" ansatz. In this
thesis we relax that assumption and investigate the most general solutions of
the Einstein-Yang-Mills system assuming spherically symmetry, a Yang-Mills
gauge group of SU(2), and zero cosmological constant. We proceed primarily by
numerically integrating the equations and find new static solutions, for both
regular and black hole boundary conditions, which are not asymptotically flat,
and attempt to classify the possible static behaviours. We develop a code to
solve the dynamic equations that uses a novel adaptive mesh refinement
algorithm making full use of double-null coordinates. We find that the "type
II" critical behaviour in the general case exhibits non-universal critical
solutions, in contrast to the magnetic case and to all previously observed type
II critical behaviour.
