The T-shaped HeI2(E0(g)(+)) van der Waals complexes populated in the HeI2(E,v(E) = 0-2,n(E) = 0 <- B,19, n(B) = 0 <- X,0,n(X)) excitation pathway have been studied. Analysis of the luminescence excitation spectra as well as the I-2(E0(g)(+) -> B0(u)(+), D0(u)(+) -> X0(g)(+), and D'2(g) -> A'2(u)) luminescence, spectra themselves has been carried out. It has been shown that the I-2(D -> X, and D' -> A') luminescence is due to HeI2(E <- B) transitions with subsequent electronic predissociation. We have determined dissociation energies of the HeI2(E,v(E) = 0-2) complexes, vibrational populations of the E, D states and branching ratios of vibrational and electronic predissociations. One can suppose that luminescence of the HeI2(E,v(E) = 0, n(E) = 0) complexes occurs. (C) 2016 Elsevier B.V. All rights reserved.