  The linear stability of a shear layer in a highly diffusive stably stratified
atmosphere has been investigated. This study completes and extends previous
works by Dudis (1974) and Jones (1977). We show that:
  (i) an asymptotic regime is reached in the limit of large thermal
diffusivity, (ii) there exists two different types of unstable modes. The
slowest growing modes correspond to predominantly horizontal motions and the
fast growing ones to isotropic motions, (iii) the physical interpretation of
the stability properties in this asymptotic regime is simple.
  Applications to the dynamics of stellar radiative zone are discussed.
