In this work we report very accurate variational calculations of the two lowest vibrational states of the D-2 and T-2 molecules within the framework that does not assume the Born-Oppenheimer approximation. The non-relativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of alpha(2) calculated as expectation values of the operators representing these effects. The v = 0 -> 1 transition energy of D-2 obtained in the calculations is compared with the transition frequency obtained from the experimental spectra. The comparison shows the need to include corrections higher than second-order in alpha to further improve the agreement between the theory and the experiment. (C) 2010 Elsevier B.V. All rights reserved.