We report on the use of electrochemical atomic-layer epitaxy (EC-ALE) to grow thin-films of the III-V compounds InAs, InSb, and an InAsxSb1-x, superlattice. EC-ALE is a method for forming compound semiconductors with improved control, compared to other electrodeposition methodologies. It involves the use of surface limited reactions to form deposits an atomic layer at a time, in a cycle. The EC-ALE cycle uses underpotential deposition (upd) to form atomic layers of each of the component elements. One cycle ideally produces one monolayer (ML) of the desired compound. Studies to optimize the InAs cycle are reported, specifically the dependence on the In and As deposition potentials. These studies show that the potentials must be adjusted for each of the first 25 or more cycles, as a contact potential between the Au substrate and the growing semiconductor develops. After deposition of this initial 'buffer layer', steady state conditions are reached, and the same potentials can be used without change, for the remaining cycles. The formation of InSb has also been investigated, and the EC-ALE growth of InSb deposits is reported for the first time. Due to a 6% lattice mismatch, and a less than fully optimized cycle, the InSb deposits on Au appear composed of 70 nm particles. By combining the InAs and InSb programs, a superlattice was formed with 41 periods, where each period involved ten cycles of InAs followed by ten cycles of InSb. X-ray diffraction (XRD) indicated a period of 5.5 nm, whereas a 7.4 nm period was expected, based on 1 ML/cycle and the (111) interplanar spacing, derived from the lattice constants for InAs and InSb. Given the stoichiometry of the resulting deposit, and the shorter periodicity observed, it appears that 1 ML/cycle of InAs was formed, while only a 1/2 ML/cycle of InSb was obtained. IR absorption measurements indicate that the deposit was red shifted relative to the lower bandgap compound, InSb (0.17 eV), which is consistent with a type II superlattice. If an alloy had been formed, the bandgap should have been a linear function of the bandgaps and relative mole fractions of InAs and InSb, or about 0.31 eV, twice the observed bandgap.