  We present here the microwave surface impedance of a high purity crystal of
$YBa_2Cu_3O_{6.99}$ measured at 5 frequencies between 1 and 75 GHz. This data
set reveals the main features of the conductivity spectrum of the thermally
excited quasiparticles in the superconducting state. Below 20 K there is a
regime of extremely long quasiparticle lifetimes, due to both the collapse of
inelastic scattering below $T_c$ and the very weak impurity scattering in the
high purity $BaZrO_3$-grown crystal used in this study. Above 20 K, the
scattering increases dramatically, initially at least as fast as $T^4$.
