Investigations of the ternary systems M/Li/Al of the heavier alkaline earth metals M = Ca, Sr, Ba yielded three new intermetallic compounds which show interesting structural relationships. Ca6LixAl23-x(x approximate to 11, Fm (3) over bar m, a = 13.430(2) Angstrom, Z = 4) crystallizes in the Th6Mn23-structure with all sites of the majority component occupied by Li and Al. Sr9Li7+xAl36-x (x approximate to 10.5, P6(3)/mmc, a = 9.638(4) Angstrom, c = 27.586(6) Angstrom, Z = 2) is a relative of the Sr3Mg13 structure, and Ba2Li3+xAl6-x (x approximate to 1.2, R (3) over bar m, a = 9.946(1) Angstrom, c = 26.992(3) Angstrom, Z = 9) is a hexagonal relative of the Th6Mn23 type. The substructures formed by Li and Al atoms are described in terms of two simple basis clusters which offer structural flexibility in their connectivity. The relative stability of the substructures has been investigated within the simple tight-binding Huckel model. Calculated energy difference curves as a function of the valence electron concentration for these networks show a pronounced stability maximum in the region of 2.5-2.7 electrons per network atom. This result fits the composition of the intermetallic compounds when applying the Zintl-Klemm concept. In addition, Mulliken population analyses of extended Huckel calculations have been used to investigate the site occupancies.