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We study the Z'-> ggg decay in the context of a left-right symmetric gaugetheory. We obtain a branching ratio BR(Z'-> ggg)=\Gamma(Z'->ggg)/ \Gamma(Z'->q\bar{q})= (1.2-2.8) x 10^{-5} for m_{Z'}=(700-1500) GeV. We also study thecontribution of a fourth fermion family. We find an enhancement in thebranching ratio for Z' masses close to the \bar{b'}b' threshold and a dip forZ' masses close to the \bar{t'}t' threshold. Using the values of the fourthgeneration quark masses allowed by electroweak precision data we obtain abranching ratio BR(Z'-> ggg)= (1-6)x 10^{-5} for m_{Z'}=(700-1500) GeV.

Z'-> ggg decay in left-right symmetric models with three and four fermion families