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The decays $\tau \rightarrow (\eta,\eta') K^{-} \nu_{\tau}$ are described inthe framework of the extended Nambu-Jona-Lasinio model. Both full anddifferential widths of these decays are calculated. The vector and scalarchannels are considered. In the vector channels, the subprocesses withintermediate $K^{*}(892)$ and $K^{*}(1410)$ mesons play the main role. In thescalar channels, the subprocesses with intermediate $K_{0}^{*}(800)$ and$K_{0}^{*}(1430)$ mesons are taken into account. Scalar channels play a lessimportant role in calculation of the full width of the decay $\tau \rightarrow(\eta,\eta') K^{-} \nu_{\tau}$. The obtained results are in satisfactoryagreement with the experimental data.

The decays $\tau \rightarrow (\eta,\eta') K^{-} \nu_{\tau}$ in the extended Nambu-Jona-Lasinio model