Single crystals of V2AlC and the new carbides V4AlC3-x and V12Al3C8 were synthesized from metallic melts. V2AlC was formed with an excess of Al, while V4AlC3-x (x approximately 0.31) and V12Al3C8 require the addition of cobalt to the melt. All compounds were characterized by XRD, EDX, and WDX measurements. Crystal structures were refined on the basis of single-crystal data. The crystal structures can be explained with a building-block system consisting of two types of partial structures. The intermetallic part with a composition VAl is a two-layer cutting of the hexagonal closest packing. The carbide partial structure is a fragment of the binary carbide VC1-x containing one or three layers. V2AlC is a H-phase (211-phase) with space group P63/mmc, Z=2, and lattice parameters of a=2.9107(6) A, and c=13.101(4) A. V4AlC3-x (x approximately 0.31) represents a 413-phase with space group P63/mmc, Z=2, a=2.9302(4) A, and c=22.745(5) A. The C-deficit is limited to the carbon site of the central layer. V12Al3C8 is obtained at lower temperatures. In the superstructure (P63/mcm, Z=2, a=5.0882(7) A, and c=22.983(5) A) the vacancies on the carbon sites are ordered. The ordering is combined to a small shift of the V atoms. This ordered structure can serve as a structure model for the binary carbides TMC1-x as well. V4AlC3-x (x approximately 0.31) and V12Al3C8 are the first examples of the so-called MAX-phases (MX)nMM' (n=1, 2, 3), where a deficit of X and its ordered distribution in a superstructure is proven, (MX1-x)nMM'.