  We consider a model of a population of fixed size N in which each individual
gets replaced at rate one and each individual experiences a mutation at rate
\mu. We calculate the asymptotic distribution of the time that it takes before
there is an individual in the population with m mutations. Several different
behaviors are possible, depending on how \mu changes with N. These results have
applications to the problem of determining the waiting time for regulatory
sequences to appear and to models of cancer development.
