The depletion kinetics of highly excited state Cr(a(5)G(J)) upon interaction with O-2, NO, N2O, and N-2 are studied in a discharged flow reactor at a He pressure of 0.7 Torr. The state lying more than 20000 cm(-1) above the ground state shows very efficient depletion by three oxygen-containing molecules, and the depletion rate constants are (119 +/- 12) x 10(-12), (124 +/- 12) x 10(-12), and (78 +/- 8) x 10(-12) cm(3) s(-1), for O-2, NO, and N2O, respectively. Five spin-orbit levels show identical rate constants. This result and the previous ones for Cr(a(5)S, a(5)D) suggest that an electron-transfer mechanism is important for the interaction of Cr with O-2 Attractive interaction to form an intermediate is also suggested for the interaction with NO and N2O. However, it is suggested that electronic energy-transfer processes are more important than chemical reactions. On the interaction with N-2, the depletion rate constant is (15 +/- 2) x 10(-12) cm(3) s(-1). This value is similar to the formation rate constants for Cr(a(5)S, a(5)D) upon the interaction with N2, and the electronic energy transfer from Cr(a(5)G(J)) to Cr(a(5)S(2), a(5)D(J)) is suggested.