Hyper,
Concrete theory is not one of my strong suits, but for a practical solution, this is what I would do:
I assume you are designing a concrete column or isolated beam loaded on both axes, and that the shear you are refering to is "diagonal tension" as opposed to "pure shear." In either case a good design would include longitudinal bars and ties.
The shear resistance of a concrete member is provided by the contribution of the concrete (Vc) and the contribution of the ties (Vs).
How the concrete contribute to the biaxial shear is not clear. I have looked for some reference to biaxial shear with no success. If we take the resultant of both shear as squareroot of (Vux^2 + Vuy^2), this resultant would be acting at an angle to the main axes of the section, and that would complicate the analysis. I would use, instead, a reduced concrete strength for each shear (Vcx and Vcy), such that Vcx = Vc*Vux/(Vux+Vuy), and Vcy = Vc*Vuy/(Vux+Vuy). Notice that this would make Vcx + Vcy = Vc.
I would design and detail the ties independently for each shear (Vux and Vuy). If there is only one tie around the section, each tie could resists both shears, since only the two sides of the loop parallel to the load are stressed.
This approach would produce a slightly conservative design.