Abstract
The calculation results of widths of the decays $$\tau \to {{a}_{1}}\pi {{\nu }_{\tau }}$$ , $$\tau \to {{K}_{1}}\pi {{\nu }_{\tau }}$$ , and $$\tau \to {{K}_{1}}K{{\nu }_{\tau }}$$ and of the cross sections of the processes $${{e}^{ + }}{{e}^{ - }} \to {{a}_{1}}\pi $$ and $${{e}^{ + }}{{e}^{ - }} \to {{K}_{1}}K$$ carried out as part of the extended Nambu–Jona-Lasinio (NJL) model are presented. Due to the absence of the appropriate experimental values, the results should be considered predictions. A comparison of the calculated widths of these tau decays to the results of other authors is carried out.