We present a status report on the research and development of high-gradient normal-conducting RF structures for the ionization cooling of muons in a neutrino factory or muon collider. High-gradient RF structures are required in regions enclosed in strong focusing solenoidal magnets, precluding the application of superconducting RF technology [1]. We propose using linear accelerating structures, with individual cells electromagnetically isolated, to achieve the required gradients of over 15 MV/m at 201 MHz and 30 MV/m at 805 MHz. Each cell will be powered independently, and cell length and drive phase adjusted to optimize shunt impedance of the assembled structure. This efficient design allows for relatively small field enhancement on the structure walls, and an accelerating field approximately 1.7 times greater than the peak surface field. The electromagnetic boundary of each cell may be provided by a thin Be sheet, or an assembly of thin-walled metal tubes. Use of thin, low-Z materials will allow passage of the muon beams without significant deterioration in beam quality due to scattering. R and D in design and analysis of robust structures that will operate under large electric and magnetic fields and RF current heating are discussed, including the experimental program based in a high-power test laboratory developed for this purpose
