To understand the potential for use of the Hf-Al-C ternary compounds, (HfC)(n)Al3C2 (Hf2Al3C4 and Hf3Al3C5) and (HfC)(n)Al4C3 (Hf2Al4C5 and Hf3Al4C6) were investigated using density functional theory, including crystal structure, electronic structure, compressibility, and elastic properties. The theoretical density of (HfC)(n)Al3C2 (4.10-4.16 g/cm(3)) is higher than that of (HfC)(n)Al4C3 (3.92-3.98 g/cm(3)), due to the smaller number of lighter Al-C layers. With increasing numbers of Hf-C layers, the Hf-C and Al-C bond lengths remain almost unchanged. In none of the compounds is there a gap around the Fermi energy (E-f), which implies they are metal-like conductors. With increasing pressure, there is greater shrinkage along the c axis than the a axis. The bond stiffness increases with increasing pressure. In general, (HfC)(n)Al3C2 has higher elastic stiffness than (HfC)(n)Al4C3, with the moduli increasing with the number of Hf-C layers. The Hf-Al-C compounds as well as the brittle Zr-Al-C compounds all have low shear moduli/bulk moduli ratio (G/B) from 0.71 to 0.78, suggesting that the G/B ratio is not always a suitable measure of ductility.