The spectral density of electrostatic fluctuations is investigated in
a plasma containing an excess of suprathermal particles. As a model fo
r the statistical distribution of the suprathermal particles, the kapp
a velocity distribution is used. It is found that the Debye length lam
bda(D) for such a plasma depends strongly on the spectral index kappa
of the velocity distribution, and can be much smaller than is commonly
found for Maxwellian plasmas. Consequently the plasma parameter g = 1
/n lambda(D)(3) call be larger, and plasma effects that depend on part
icle discreteness more important. than for a Maxwellian plasma. Conseq
uently levels of fluctuation are higher, and their extent in wavenumbe
r and frequency greater, in plasmas containing suprathermals. Results
for a number of different 'concentrations' of suprathermal particles a
re discussed and interpreted in terms of the normal- as well as transi
ent-mode behaviour of the plasma. Both the cases T-e much greater than
T-i and T-e = T-i, as well as kappa(e) much less than kappa(i) and ka
ppa(e) much greater than kappa(i), are investigated.