  We show that, in string theory, the quantum evaporation and decay of black
holes in two-dimensional target space is related to imaginary parts in
higher-genus string amplitudes. These arise from the regularisation of modular
infinities due to the sum over world-sheet configurations, that are known to
express the instabilities of massive string states in general, and are not
thermal in character. The absence of such imaginary parts in the matrix model
limit confirms that the latter constitutes the final stage of the evaporation
process, at least in perturbation theory. Our arguments appear to be quite
generic, related only to the summation over world-sheet surfaces, and hence
should also apply to higher-dimensional target spaces.
