Recent experiments have demonstrated that well-ordered one-dimensional column nanostructures can be formed via self-assembly in a variety of two-component epitaxial systems, including diluted magnetic semiconductors and high-TC superconductors. Here we use kinetic Monte Carlo simulations based on a (1+1)-dimensional lattice model to study the morphological evolution of strain-free two-component films during epitaxial growth in the nonequilibrium kinetic regime. Our simulations show that columnlike nanostructures are only formed in the system when the interatomic bond energies EAA, EBB, and EAB satisfy the inequality of EAB