A chiral U(3) × U(3) Lagrangian, containing besides the usual meson fields their first radial excitations, is considered. The Lagrangian is derived by bosonization of the Nambu-Jona-Lasinio (NJL) quark model with separable nonlocal interactions. The spontaneous breaking of chiral symmetry is governed by the NJL gap equation. The first radial excitations of the kaon, K^* and are described with the help of three form factors. The values for the decay widths of the processes K^*´ K,K^*´ K^*, K^*´ K, ´ K^*K, ´K, K´ K, K´ K^* and K´ K2 are obtained in qualitative agreement with the experimental data.