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NEMS (nanoelectromechanical systems) loom beyond the MEMS horizon as the new frontier in miniaturization. Nanorobots and other NEMS are expected to find revolutionary applications in science, engineering and everyday life. Until now, nanostructures have been built primarily in 2D, because of the difficulties of 3D fabrication. This paper describes a promising approach to the construction of 3D nanostructures by working in successive layers, much like the rapid prototyping techniques used in the macroscopic world. Each object nanolayer is built by nanomanipulation, or possibly by programmed self-assembly, and then surrounded by a sacrificial layer that planarizes the sample and serves as a substrate for the deposition of the next object nanolayer. Initial experimental results which show that the approach is feasible are presented.