In this paper, gravothermal oscillations are investigated in multicomponent star clusters which have power-law initial mass functions (IMFs). For the power-law IMFs, the minimum masses (mmin) were fixed and three different maximum stellar masses (mmax) were used along with different power-law exponents (α) 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 multicomponent gas code spedi. The total mass (Mtot) is seen to give an approximate stability condition for power-law IMFs with fixed values of mmax and mmin independent of α. The value Mtot/mmax ≃ 12 000 is shown to give an approximate stability condition which is also independent of mmax, 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.