The dependence of the intensities of atomic lines and molecular bands emitted in the afterglow of a helium discharge on the electron temperature is used to identify the processes in which states of He{star operator} and He₂^* are populated. It is established that the formation of He^* atoms (n = 3, 4) in decaying helium plasma occurs principally on account of the associative recombination of vibrationally excited He₂⁺ ions and electrons. Analysis of the experimental reuslts leads to the conclusion that the distribution of the molecular ions He₂⁺ over vibrational states is strongly nonequilibrium.