  We study the collision frequencies of charged particles in the complex
plasmas with the non-Maxwellian velocity distributions. The average collision
frequencies of electron-ion, electron-electron and ion-ion are derived in the
two-parameter (r,s) and the three-parameter (a,r,s) velocity distributions,
respectively. We show that these average collision frequencies in the complex
plasmas depend strongly on the parameters in the non-Maxwellian distributions
and thus are significant deviations from those in the plasmas with a Maxwell
velocity distribution. Numerical analyses are made of the effects of the
parameters on the average collision frequencies. The results have important
effect on transport coefficients and their properties of charged particles in
the highly ionized complex plasmas with the non-Maxwell distributions.
