The relaxation rates of Ne//2** plus molecular ions in collisions with electrons and neon atoms are found by analyzing the spectral line intensities for certain transitions for atomic neon as a function of the density of neutral atoms, the electron density and temperature, and the time in a decaying plasma. The coefficients of dissociative recombination for Ne//2** plus ions are found as a function of temperature. The Boltzmann distribution with a temperature T equal to that of the surrounding ions is found to differ greatly from the vibrational distribution of the molecular ions.