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Trajectory surface hopping calculations are reported for the Li + Li 2 (X 1 Σ g +) dissociation reaction over the range of translational energies 13 e E tr /kcal mol-1 e 80. Both potential energy surfaces for ground doublet Li 3 , which have been modeled from the double many-body expansion method (DMBE III), have been employed in the dynamics calculations. For the initial internal state (V) 0, j) 10), the behavior of the dissociative cross sections as a function of translational energy shows that nonadiabatic effects are important over the whole range of energies studied. Concerning the role of initial vibration, it has been found that, for E tr) 25 kcal mol-1 and j) 10, the adiabatic dissociative cross sections are enhanced as V increases from 0 to 20, while the nonadiabatic ones just slightly increase with the vibrational quantum number. of alkali atoms and molecules M′ + M 2 (V,j) (M, M′) Li, Na, K, Rb, Cs) have been much studied from both the experimental and theoretical points of view. 14-18 In turn, the DMBE III potential energy surface has previously been employed for adiabatic studies 19 of the Li + Li 2 exchange reaction and most