Density functional calculations with simulated annealing have been performed for clusters of aluminum Al(n) and gallium Ga(n) up to n = 10. There are many local minima in the energy surfaces, with a rich variety of structures and spin multiplicities. With increasing cluster size we find transitions from planar to nonplanar structures at n = 5, and to states with minimum spin degeneracy at n = 6. Isomers (n greater-than-or-equal-to 5) with buckled planar structures reminiscent of the layers in crystalline alpha-gallium are generally less stable than ''three-dimensional'' isomers. All structures show regular patterns of bond and dihedral angles. Systematic differences between Al and Ga clusters-bonds in the latter are shorter and bond angles closer to 90-degrees - can be understood in terms of atomic properties. Trends in binding and ionization energies are compared with experiment and with the predictions of other calculations.