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In the terahertz (THz) band, high-harmonic operations of gyro-devices are attractive for the great potential to reduce the required external magnetic field strength, which is proportional to the oscillation frequency but inversely proportional to the operational harmonics. This thesis focuses on the study of high-harmonic operation of the gyro-devices. Specifically, a high-harmonic large-orbit gyrotron (LOG) and the output system for a gyro-multiplier will be investigated. Firstly, the complex-cavity gyrotron, which is the foundation of the gyro-multiplier scheme, is studied by programming and computer simulation. The computer code and the complex-cavity operation are then verified by three-dimensional (3D) Particle-In-Cell (PIC) simulation. The code can be used as a preliminary design tool of the beam-wave interaction cavity for both the LOG and the gyro-multiplier. Secondly, a high-harmonic LOG operating with the TEm,1,1 modes (m=4-9) has been designed and investigated. It is shown that by proper choice of the operation parameters, selective excitation of oscillation from the fourth to the ninth harmonic of the electron cyclotron resonance can be achieved with kW-level output power from 230 GHz to 465 GHz. By enabling the high-harmonics operation, the required external magnetic field strengths are reduced to the range between 2.6 T to 3.1 T. The parameter variation study is also performed to provide a general conclusion of the high-harmonic LOGs operation. Thirdly, this thesis presents the investigation of a quasi-optical output system for a fourth-harmonic gyro-multiplier in the THz band. A dual-harmonic quasi-optical mode converter (DQMC) and a frequency selective surface (FSS) are employed within this system. It is shown that the optimal design of the DQMC requires a special mode selection in the gyro-multiplier. The high-pass FSS is designed, fabricated and experimentally verified by a THz-TDS system. It is demonstrated that the designed FSS is capable of handling the high-power output from the gyro-multiplier.