An Au alloy bonding wire which comprises an Au alloy matrix containing high purity Au and at least one of high purity Pd and Pt in a total amount of 0.05 to 2 mass %, and, incorporated in the matrix as a trace element, Mg in an amount of 10 to 100 mass ppm, Ce in an amount of 5 to 100 mass %, and at least one of Be, Y, Gd, La, Eu and Si in an amount of each element of 5 to 100 mass % and in a total amount of Be to Si of 5 to 100 mass ppm; an Au alloy bonding wire which comprises the above Au alloy matrix and, incorporated in the matrix as a trace element, Mg and Be and at least one of Y, La, Eu and Si; an Au alloy bonding wire which comprises the above Au alloy matrix and, incorporated in the matrix as a trace element, Mg in an amount of 10 to 100 mass ppm, Si in an amount of 5 to 30 mass ppm, Be in an amount of 5 to 30 mass ppm, and at least one of Ca, Ce and Sn in an amount of 5 to 30 mass ppm. The above bonding wire is a fine diameter Au alloy bonding wire which has a desired strength, exhibits good binding characteristics and good stability for a long period of time, and is improved in the circularity of a pressed ball and the sphericity of a molten ball.