The binary alkaline earth trielides of the composition AIIMIII 2 exhibit a puzzling variety of structure types ranging from electron precise Zintl compounds like CaIn2 and KHg2 (both with networks of four-bonded M− entities) and the AlB2 structure type (with graphite analogue M sheets) to the cubic Laves phases e. g. of CaAl2. The examination of the phase stabilities of mixed compounds AM1IIIx M2III2−x of two trielides allows to separate the stability ranges in a structure map by taking the electronegativity differences of MIII and AII (Δ EN) and the radius ratios (RR = rM/rA) into account: The CaIn2-type is stable at comparatively large RR, for example over the whole range CaGa2 -CaIn2 and even up to CaAl0.6Ga1.4 and CaAl1.2In0.8, and in SrIn2, together with a limited substitution of In by Al or Ga. The KHg2-type is observed in a region of lower RR: In BaIn2, a substitution of In by 50% Al and 30% Ga is possible without a general structure change, in SrAl2 this holds for a content of up to 50% In. At high Δ EN and low RR values (e. g. Sr/Ba-Ga), the ideal AlB2 structure type exhibits a distinct stability range; only for small RR around CaAl2 the MgCu2-type is stable. FP-LAPWband structure calculations of the binary trielides allow to explain the structural changes qualitatively. In the case of the electron precise phases forming the CaIn2, KHg2 or AlB2 structure type, details of the bonding situation (such as M-M distances) as well as differences to other isoelectronic compounds can be rationalized taking the incomplete charge transfer from the alkaline earth towards the triel elements into account. This causes a partial depopulation of some of the bonding and a population of predominantly antibonding states.