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The possibility of a significant effect of exotic particles on theZ'->\gamma\gamma\gamma{} and Z->\gamma\gamma\gamma{} decays is investigated inthe context of the minimal 331 model. This model, which is based in theSU_C(3)xSU_L(3)xU_X(1) gauge group, predicts the existence of many exoticcharged particles that can significantly enhance the decay widths. It is foundthat the standard model prediction for the Z->\gamma\gamma\gamma{} decayremains essentially unchanged, as the new physics effects quickly decouples. Onthe other hand, it is found that the contributions of the new exotic quarks andgauge bosons predicted by this model lead to a branching fraction for theZ'->\gamma\gamma\gamma{} decay of about 10^(-6), which is about three orders ofmagnitude larger than that of the Z->\gamma\gamma\gamma{} decay.

Decays Z' -> \gamma\gamma\gamma{} and Z -> \gamma\gamma\gamma{} in the minimal 331 model