  The definition of thermal relaxation time is extended to chemically
non-equilibrated quark-gluon plasma and the chemical non-equilibrated thermal
relaxation times for partons are calculated using the non-equilibrium Debye
mass as the infrared regulator. The dependence of the thermal relaxation time
on the fugacity is given and the influence of the chemical non-equilibration is
discussed. We find that there are threshold fugacities $\lambda_g^*$ and
$\lambda_q^*$ for gluons and quarks. For \lambda_g < \lambda_g^* (\lambda_q <
\lambda_q^*), \tau_g^{NEQ}/\tau_g^{EQ} (\tau_q^{NEQ}/\tau_q^{EQ}) decreases
strongly with increasing fugacity, while for $\lambda_g > \lambda_g^*
(\lambda_q>\lambda_q^*$), the ratios are almost 1. It is shown that there is
also the two-stage equilibration in a chemically non-equilibrated plasma. We
also discussed the effect of using the non-equilibrium Deby mass as the
infrared cutoff.
