We propose several designs of nonlinear optical waveguides based on quaternary III-V semiconductors AlGaAsSb and InGaAsP. These semiconductor materials have been widely used for laser sources. Their nonlinear optical properties, however, yet remain unexplored, while the materials definitely hold promise for nonlinear photonics on-a-chip. The latter argument is based on the fact that III-V compounds tend to exhibit high values of the nonlinear optical susceptibilities, while the nonlinear absorption in these materials can be minimized in the wavelength range of interest through a proper selection of the material composition. We present the modal analysis for the designed waveguide structures and show that the effective mode area much less than can be achieved through a design optimization in each of the two compounds. We also present specific waveguide designs that demonstrate zero dispersion at the wavelengths of interest. The designed AlGaAsSb and InGaAsP waveguides are thus expected to demonstrate high values of the nonlinear coefficient and efficient nonlinear optical interactions.