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A genetic equilibrium occurs when an allele within a gene pool is not changing in frequency (i.e. evolving). For this to be the case, evolutionary forces acting upon the allele must be equal and opposite. The only basic requirement is that the population be large enough that the effects of genetic drift are minimised. One example is Hardy-Weinberg equilibrium. For more see heterozygote advantage, fixation, mutation-selection balance, negative frequency-dependent selection etc. There may be inbreeding as this reduces heterozygosity but does not cause evolution.
