  In this paper, gravothermal oscillations are investigated in multi-component
star clusters which have power law initial mass functions (IMF). For the power
law IMFs, the minimum masses ($m_{min}$) were fixed and three different maximum
stellar masses ($m_{max}$) were used along with different power-law exponents
($\alpha$) ranging from 0 to -2.35 (Salpeter). The critical number of stars at
which gravothermal oscillations first appear with increasing $N$ was found
using the multi-component gas code SPEDI. The total mass ($M_{tot}$) is seen to
give an approximate stability condition for power law IMFs with fixed values of
$m_{max}$ and $m_{min}$ independent of $\alpha$. The value $M_{tot}/m_{max}
\simeq 12000$ is shown to give an approximate stability condition which is also
independent of $m_{max}$, though the critical value is somewhat higher for the
steepest IMF that was studied. For appropriately chosen cases, direct N-body
runs were carried out in order to check the results obtained from SPEDI.
Finally, evidence of the gravothermal nature of the oscillations found in the
N-body runs is presented.
