  The problem of disorder seeks to determine a stopping time which is as close
as possible to the unknown time of ``disorder'' when the observed process
changes its probability characteristics. We give a partial answer to this
question for some special cases of Levy processes and present a complete
solution of the Bayesian and variational problem for a compound Poisson process
with exponential jumps. The method of proof is based on reducing the Bayesian
problem to an integro-differential free-boundary problem where, in some cases,
the smooth-fit principle breaks down and is replaced by the principle of
continuous fit.
