The gyrocon is a high-power, high-efficiency amplifier that operates by deflection modulation of an electron beam. The bunching is better than that in a klystron, especially for very high powers and UHF frequencies, so the overall efficiency and the maximum output power can be higher than in a klystron. The present theory includes the effects of large signals, space charge, and finite beam size. The equations of motion are relativistically correct, and the space-charge fields are correct to first order in v/c. The theory is derived and a computer code to solve these equations is discussed. The code is then used to obtain several specific examples of gyrocon designs that have significant advantages over klystrons or gridded tubes in the 0.2-to 1.0-GHz frequency range. Several embodiments of the gyrocon are possible, and we discuss the radial style and the spherical style in this report. The radial style has a bender magnet to increase the deflection of the beam, whereas the spherical gyrocon does not employ the bender magnet. The optimium frequency range for the spherical gyrocon is from 1.0 to 2.5 GHz. The progress to date on the design, construction, and testing of a 650-kW output, 450-MHz prototype gyrocon is discussed. We had planned to have this gyrocon operating by the end of FY-79; however, two of the major subcontractors have had unexpected problems in producing the deflection and output cavities. The experimental program therefore will continue into FY-80. The sagacity of the early R&D investment, which proved the device feasibility by developing a sound theory and a prototype design, has been verified by receipt of funds from other agencies with urgent application needs. :.