The systems AeAl(2-x)Mg(x) (Ae = Ca, Sr, Ba) display electron concentration induced Laves phase structural changes. However, the complete sequence MgCu2 --> MgNi2 --> MgZn2 with increasing x (decreasing electron count) is only observed for Ae = Ca. Compounds SrAl2-x,Mg-x, (0 < X less than or equal to 2) and BaAl2-x,Mg-x, (X = 0.85 and 2.0) were synthesized and structurally characterized by X-ray diffraction experiments. For the Sr system the structural sequence CeCu2 --> MgNi2 --> MgZn2 occurs with increasing Mg content x. Thus, larger Sr does not allow the realization of the MgCu2 structure at low x. For Ae = Ba a binary compound BaAl2 does not exist, but more Ba-rich Ba7Al13 forms. The reinvestigation of the crystal structure of Ba7Al13 by selected area and convergent beam electron diffraction in a transmission electron microscope revealed a superstructure, which subsequently could be refined from single X-ray diffraction data. The formula unit of the superstructure is Ba21Al40 (space group P31m, Z = 1, a = 10.568(l) Angstrom, c = 17.205(6) Angstrom). In Ba21Al40 a size match problem between Ba and Al present in Ba7Al13 is resolved. The structure of Ba7Al13 (Ba21Al40) can be considered as a Ba excess variant of the hexagonal MgNi2 Laves phase type structure. An incommensurately modulated variant of the MgNi2 structure is obtained for phases BaAl2-xMgx with x = 0.8-1. At even higher Mg concentrations a structural change to the proper MgZn2 type structure takes place.