Many space plasmas have an excess of superthermal particles and can be modelled by a &kgr;-distribution. While&kgr;→∞yields the Maxwellian, a low value of &kgr; describes a power-law distribution with a strongly accelerated, hard spectrum. Wave studies require the generalized plasma dispersion function, which may be expressed in terms of a hypergeometric function, making it easily usable. We review studies of waves in &kgr;-distribution plasmas, focusinginter aliaon applications to space plasmas. Wave behavior for low-&kgr; plasmas is significantly different from that found for Maxwellian plasmas. ©2000 American Institute of Physics.