Abstract <p>Protons (and heavier ions) with anisotropic velocity distributions and nonthermal deviations from the Maxwellian distribution are frequently observed in the solar wind in the magnetosphere and at different altitudes. The present paper investigates the influence of hyperthermal populations on the main characteristics of mirror and firehose instabilities in a rarefied gravitating plasma using the Chew–Goldberger–Low (CGL) equations modified to account for the effect of anisotropic thermal conductivity. The plasma distribution anisotropy, including hyperthermal populations, is modeled using bi-kappa functions, and new dispersion relations for the kappa distributions are derived using the modified plasma distribution function. An important feature of the proposed approach is that some terms introduced by higher-order moments have the same order as terms in the classical CGL equations. These terms lead to modified conditions for mirror and firehose instabilities. However, in the limit of vanishing zero heat flux, the firehose instability condition in a heat-conducting plasma remains unchanged. Deviations associated with superthermal tails from the standard cosmic Maxwellian plasma dispersion may ultimately be used to estimate the presence of superthermal populations during solar flares and in the magnetosphere.</p>