Estimates are made of the rates for the de-excitation of (π^-, α) and (K^-, α) atoms in liquid helium. An estimate is also made of the rate of nuclear capture of K^- mesons from high s states. The calculated Auger and radiative rates give total cascade times which are roughly 5 times shorter than the experimental values. The approximations which are used are such that this is regarded as satisfactory agreement. For principal quantum number 21 ≤ n ≤ 24 the Auger rate for (K^-, α) atoms is approximately equal to the rate for nuclear absorption. The calculations indicate that the amount of K^- absorption from high s states may not be negligibly small.