  The first radial excitations of axial-vector mesons are considered in the
framework of the extended $U(3)\times U(3)$ Nambu--Jona-Lasinio model. We
calculate the mass spectrum of $a_1$, $f_1$, and also strange axial-vector
mesons. For description of radially excited states we used the form factors of
polynomial type of the second order in transverse quark momentum. For the
ground- and the excited-state mesons consisting of light quarks we have
calculated the widths of a number of strong and radiative decays. We got
satisfactory agreement with experimental data for the ground states. A set of
predictions for the excited states of mesons is given.
