  First radial excitations of the isoscalar and isovector scalar mesons
f_0(400-1200), f_0(980) and a_0(980) are investigated in the framework of a
nonlocal version of a chiral quark model of the Nambu--Jona-Lasinio type. It is
shown that f_0(1370), f_J(1710) and a_0(1450) are the first radially excited
states of f_0(400-1200), f_0(980) and a_0(980) which are ground states of the
scalar meson nonet. The mesons' masses and strong decay widths are calculated.
The scalar resonance f_0(1500) is supposed to be a glueball. The status of
K_0^*(1430) is discussed.
