We have carried out a quasiclassical trajectory study of the O + NO(v) energy transfer process using DMBE potential energy surfaces for the ground-states of the (2)A' and (2)A '' manifolds. State-to-state vibrational relaxation rate constants have been computed over the temperature range 298 and 3000 K and initial vibrational states between v = 1 and 9. The momentum-Gaussian binning approach has been employed to calculate the probability of the vibrational transitions. A comparison of the calculated state-to-state rate coefficients with the results from experimental studies and previous theoretical calculations shows the relevance of the 1 (2)A '' potential energy surface to the title vibrational relaxation process.