The design and simulation studies establish what the various accelerator subsystems, and their components, must do. Some of the components required for Neutrino Factories and Muon Colliders are beyond the present state-of-art. Hence within MAP there is a technology development program to prototype and test the most demanding components: those whose performance is beyond what has been done before. Muon Colliders are particularly challenging. The technologies that require R&D include radiofrequency cavities that operate in strong magnetic fields, high field solenoid magnets with unusual geometries (twisted into a helix), very high field solenoid magnets, possibly using high temperature superconductors, and liquid mercury jet proton targets, with the jet injected into a high field solenoid.