The formation of q (q) over bar resonances lying on the leading Regge
trajectories in the (N) over bar N system is studied in the quark-gluo
n string model. The model predicts strong suppression of the decays of
q (q) over bar states into (N) over bar N pairs in relation to two-me
son modes. Our analysis shows that the contributions of the resonances
f(4)(2050) (I(G)J(PC) = 0(+)4(++)), rho(5)(2240) (I(G)J(PC) = 1(+)5(-
-)) and f(6)(2510) (I(G)J(PC) = 0(+)6(++)) to the processes of two-mes
on (N) over bar N annihilation((p) over bar p --> pi pi, (K) over bar
K...) are about 1% of the corresponding experimental integrated cross
sections.