We investigate non-equilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp crossover) at the same temperature $T_{rm u}=0.282 J$ as for static properties due to unbinding of $mathbb{Z}_2$-vortices. We show that starting from the high-temperature initial state, due to presence of $mathbb{Z}_2$-vortices in the considering system, in a broad temperature range $T<T_{rm u}$ the dynamic properties in the intermediate time range are similar to those of two-dimensional XY model below Berezinskii-Kosterlitz-Thouless transition. The interaction of $mathbb{Z}_2$-vortices with spin-wave degrees of freedom does not emerge until rather long times.
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