Single crystals of the ternary borides Cr2AlB2, Cr3AlB4, Cr4AlB6, MoAlB, WAlB, Mn2AlB2, and Fe2AlB2 were grown from the elements with an excess of Al. Structures were refined by X-ray methods on the basis of single crystal data. All compounds crystallize in orthorhombic space groups. In each case boron atoms show the typical trigonal prisms BM6. The BM6-units are linked by common rectangular faces forming B-B-bonds. Thus, zigzag chains of boron atoms are obtained for MoAlB, WAlB, and M2AlB2 (M = Cr, Mn, Fe); chains of hexagons for Cr3AlB4; and double chains of hexagons for Cr4AlB6. The same subunits are known for the binary borides CrB, Cr3B4, Cr2B3, and β-WB, too. The boride partial structures are separated by single layers of Al-atoms in the case of the chromium compounds and double layers for WAlB, i.e., W2Al2B2. All crystal structures can be described using a unified building set principle with quadratic 4(4)-nets of metal atoms. The different compositions and crystal structures are obtained by different numbers of metal layers in the corresponding parts according to the formula (MB)2Aly(MB2)x. This principle is an extension of a scheme which was developed for the boridecarbides of niobium. Furthermore, there is a close similarity to the group of ternary carbides MAl(MC)n, so-called MAX-phases. Therefore, they might be named as "MAB-phases". The pronounced two-dimensionality and the mixture of strong covalent and metallic interactions make MAB-phases to promising candidates for interesting material properties. All compositions were confirmed by EDX measurements. Additionally, microhardness measurements were performed.