Ion distributions in the near-Earth magnetotail often deviate significantly from a bi-Maxwellian, the form usually assumed in previous studies of instability in this region of space. Here the electromagnetic dispersion equation for propagation parallel to the background magnetic field is derived from the linearised Vlasov equation for both the generalised bi-Lorentzian (kappa) distribution and a crescent shaped distribution. For the hot drifting proton distributions in the near Earth magnetotail it is found that increasing deviation from bi-Maxwellian toward bi-Lorentzian and crescent shaped forms reduces the maximum temporal growth rates and extends the range of wavenumbers and frequencies where instability occurs. The extension of the range of unstable wavenumbers has the significant effect of increasing convective growth rates in the vicinity of the crossover frequency. ¿ 1997 American Geophysical Union