EuAgxAl11-x phases adopting the BAHg(11)-type structure (space group Pm (3) over barm, Z = 3) were synthesized with high yield by arc melting a mixture loaded as "EuAg3 Al-5(7) (5)" and annealing at 500 degrees C for 40 days This phase has it very narrow phase width around EuAg4 Al-0(7) (0); and it is unstable 600 and 700 degrees C, at which it transforms into other phases. Magnetometry indicates that Eu is divlaent, which gives the valence electron concentration per Ag/Al atom as 2 45 e(-)/atom, higher than in the BaCd11-type phases in the Eu-Ag-Al system (2 10-2 30 e(-)/atom) First pinciples electronic structure calculations, using a computational model structure built by simulating the crystallographic results as well as maximizing the number of heteroatomic (Ag-Al) contacts, can explain why the cubic BaHg11-type structures is favored at higher valence electron concentration than the tetragonal BaCd11-type structure.