The dependences of the I-2(E0(g)(+), nu(E), J(E)-->(I2(X))D0(u)(+), nu(D), J(D)) transition rate constants on the vibrational nu(E), nu(D), rotational J(E),J(D) quantum numbers, energy gaps, and Franck-Condon factors of the combined levels have been studied in the range nu(E) = 8-23. The extremely long-range near-resonance I-2(E, nu(E)-->D-I2(X), nu(D)) process as well as nonresonant transitions, corresponding to the energy loss up to DeltaE = 240 cm(-1) (approximately three quanta of vibrational energy), have been observed. Total cross-section of the latter is up to 12 times less than the maximum one of the extremely long-range transition. It has been shown that cross-sections of the processes are independent of initial JE number. The u <----> g and DeltaOmega = 0 propensity rules are valid in the I-2(E)-->I-I2(X)(2) (ion-pair states) transitions. The vibrational and rotational populations of the D state levels depend on nu(E) and DeltaE. Mechanism of the processes under study has been discussed. It has been shown that essentially nonresonant transitions occur after a mutual 1,(E) and 12(X) capture in orbiting-controlled collision complex. Maybe, one has to take into account relativistic (magnetic) interactions for description of the extremely long-range transitions. (C) 2002 Elsevier Science B.V. All rights reserved.