Experimental work is being performed by collaborators at LLNL, SLAC, and LBL to investigate relativistic klystrons as a possible rf power source for future high-gradient accelerators. We have learned how to overcome or previously reported problem of high power rf pulse shortening and have achieved peak rf power levels of 330 MW using an 11.4-GHz high-gain tube with multiple output structures. In these experiments the rf pulse is of the same duration as the beam current pulse. In addition, experiments have been performed on two short sections of a high-gradient accelerator using the rf power from a relativistic klystron. An average accelerating gradient of 84 MV/m has been achieved with 80-MW of rf power.