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 beta-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)(2)Al-y(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.