[en] Several narrow resonance features in the system of two K_S mesons were found on the basis of experimental data obtained by using the 6-m spectrometer of the Institute of Theoretical and Experimental Physics (ITEP, Moscow). Three resonances, X(1070), X(1545), and f_J(2220), are considered in the present study. An interference with the background is observed for the X(1545) resonance. It is shown that X(1070) and f_J(2220) resonances are produced under nearly identical kinematical conditions characterized by high transverse momenta and the production of accompanying extra pions.