Single crystals of the new ternary carbides Ta4AlC3 and Ta3AlC2 were synthesized from molten aluminum and characterized XRD, EDX, and WDX measurements. Crystal structures were refined for the first time on the basis of single-crystal data. Both compounds crystallize in a hexagonal structure with space group P6(3)/mmc and Z = 2. The lattice constants are a = 3.1131(3) A and c = 24.122(3) A for Ta4AlC3 and a = 3.0930(6) A and c = 19.159(4) A for Ta3AlC2. The crystal structures can be explained with a building block system consisting of two types of partial structures. The intermetallic part with a composition TaAl is a two layer cutting of a hexagonal closest packing. The carbide partial structure is a fragment of the binary carbide TaC (NaCl type). It consists of three (Ta4AlC3) or two layers (Ta3AlC2) of CTa6-octahedra linked via common corners and edges. Both compounds are members of the series (TaC)(n)TaAl. The crystal quality of Ta3AlC2 is improved by using a Al/Sn melt for crystal growth leading to small quantities of Sn in the crystal: Ta3Al1-xSnxC2, x approximate to 0.04. On the basis of reliable data a detailed discussion of structural parameters is possible. According to the building principle structure models can be developed for the whole series (MX)(n)MM' including coordinates for all atoms.