We study the evolution of an initially cold, spherically symmetric sys
tem of self-gravitating particles. This is done through numerical simu
lation using a simple shell code and through an analysis of the ''scal
ed'' collisionless Boltzmann and Poisson equations. At early times the
system undergoes selfsimilar collapse of the type described by Fillmo
re and Goldreich and by Bertschinger. This stage of what is essentiall
y phase mixing soon gives way to a period of more efficient relaxation
driven by an instability in the similarity solution. We also discuss
the connection between initial conditions and the final distribution f
unction.