  We prove the existence of a unique family of non-oscillatory
(purely-imaginary) polar quasinormal resonances of rapidly-rotating Kerr black
holes. These purely imaginary resonances can be expressed in the compact form:
w_n=-i2*pi*T_{BH}*(l+1+n), where T_{BH} is the black-hole temperature, l is the
spheroidal harmonic index of the mode, and n=0,1,2,... is the resonance
parameter. It is shown that our analytical results for the black-hole resonance
spectrum agree with new numerical data that recently appeared in the
literature.
