It is always one of directions that apply the waveguide and coaxial line with slotted structure to the microwave apparatus which the domestic and foreign scholars study. The waveguide and coaxial line with slotted structure is a waveguide structure which is always used for relativistic back wave oscillator (RBWO) or oscillator and cyclotron auto-resonance maser amplifier(CARM).These have demonstrated to be a high power, high gain coherent radiation source in millimeter and submillimeter waves. Potential applications include plasma heating, high-density communications, deep-space radar, high-gradient linear colliders, atmospheric sensing, and tracking of space debris. At the same time, the investigations on the propagation characteristics of waveguides are an important major in electromagnetic theory. Based on its forward position and tremendous practical value, the thesis mainly focuses on the analysis and study of the propagation characteristics of the waveguide and coaxial line with slotted structure.Firstly, in this thesis, the current situations on waveguide and coaxial line and its investigations around the world and the forward position and practical value about it are studied.Secondly, the classification of the waveguide is made and the methods commonly treated with waveguide are given. The electromagnetic fields and propagation characteristics of the rectangular waveguide, the circular waveguide and circular coaxial lines have been studied, and its mode eigenequation is derived as well. To reveal the propagation characteristics of these cylindrical waveguides and coaxial lines, some numerical results of the modes in these waveguides and coaxial lines are presented.Thirdly, by employing the method of field matching, the propagation characteristics of the inner slotted coaxial line are analyzed. The electromagnetic fields are derived in the coaxial line with inner slotted structures. Then the mode eigenequations are derived. To reveal the propagation characteristics of the inner slotted coaxial line, some numerical results of the modes in the waveguide are presented to analyze the propagation characteristics influenced by their structures, etc.Finally, the propagation characteristics of the outer slotted coaxial line are analyzed. The electromagnetic fields and its mode eigenequations are derived in the coaxial line with outer slotted structures. When the radius of the inner conductor equals zero, the outer slotted coaxial line becomes an outer slotted cylindrical waveguide, and its eigenequation is derived as well. Numerical results are presented to reveal the propagation characteristics of influenced by their structures, etc.Through our investigations, we believe it is helpful for other researchers to study the design and application of the waveguide and coaxial line with slotted structure.