We examined several possible fluxional pathways for hexameric alkyllithiums, performing ab initio SCF calculations on the model compounds octahedral Li6H6, Li6H4(CH3)2, and Li6(CH3)6. The lowest energy structures for these compounds had an approximately octahedral arrangement of the lithiums, with the H or CH3 ligands occupying six of the eight faces. The two empty faces were trans related. A concerted mechanism in which each of two ligands on opposite sides of the octahedron moves to an empty face was found to have a low energy barrier. The midpoint structures of this pathway for both Li6H6 and Li6H4(CH3)2 were symmetric or undistorted, whereas the midpoint structure for Li6(CH3)6 was quite distorted. These results are discussed in the light of similar findings on Li6 clusters. The adequacy of using 3-21G as a basis set for investigating alkyllithium geometries is also discussed.