Aluminum brazing alloys for assembling aluminum heat exchangers by brazing which consist essentially of 4.5 to 13.5% of Si, 0.05 to 0.5% of Ca and the balance essentially Al and, additionally may contain Mg in the range of 0.3 to 3.0% or at least Cu component of 2.3 to 4.7% of Cu and 9.3 to 10.7% of Zn. The aluminum brazing alloys have an excellent brazability and provide high strength brazed joints with highly refined microstructure. Such superior properties make the brazing alloys especially suited for the fabrication of superhigh pressure heat exchangers.