The spectral density of electrostatic fluctuations is investigated in a plasma containing an excess of suprathermal particles. As a model for the statistical distribution of the suprathermal particles, the kappa velocity distribution is used. It is found that the Debye length λD for such a plasma depends strongly on the spectral index κ of the velocity distribution, and can be much smaller than is commonly found for Maxwellian plasmas. Consequently the plasma parameter g=1/nλ3D can be larger, and plasma effects that depend on particle discreteness more important, than for a Maxwellian plasma. Consequently, levels of fluctuation are higher, and their extent in wavenumber and frequency greater, in plasmas containing suprathermals. Results for a number of different ‘concentrations’ of suprathermal particles are discussed and interpreted in terms of the normal- as well as transient-mode behaviour of the plasma. Both the cases Te[Gt ]Ti and Te=Ti, as well as κe[Lt ]κi and κe[Gt ]κi, are investigated.