Hexagonal mesophases made of oil-swollen surfactant-stabilized tubes arranged on a triangular lattice in water and doped with metallic salts are used as templates for the radiolytic synthesis of nanostructures. The nanostructures formed in this type of soft matrix are bimetallic palladium-platinum porous nanoballs composed of 3D-connected nanowires, of typical thickness 2.5 nm, forming hexagonal cells. Using electron microscopy and small-angle X-ray scattering it is demonstrated that the pore size of the nanoballs is directly determined by the diameter of the oil tube of the doped mesophases, which is varied in a controlled fashion from 10 to 55 nm. Bimetallic nanostructures composed of various proportions of palladium and platinum can be synthesized. Their alloy structure is studied using X-ray photoelectron spectroscopy, energy-dispersive X-ray spectroscopy, and high-angular dark field scanning transmission electron microscopy experiments. The templating approach allows the synthesis of bimetallic nanoballs of tunable porosity and composition.