  We study operators of Kramers-Fokker-Planck type in the semiclassical limit,
assuming that the exponent of the associated Maxwellian is a Morse function
with a finite number $n_0$ of local minima. Under suitable additional
assumptions, we show that the first $n_0$ eigenvalues are real and
exponentially small, and establish the complete semiclassical asymptotics for
these eigenvalues.
