The coherent transponder is part of the telemetry and telecommand (TMTC) subsystem of a spacecraft. The function of a transponder is to receive Radio Frequency (RF) signal odulated with telecommand and ranging information from the Telemetry, Tracking and Control (TTC) ground station, process it, and transmit RF signals (at a different frequency) modulated with the telemetry and ranging information to the TTC station. The coherent type transponder, however, makes the direct measurement of range rate between the satellite and the ground station possible. In the coherent transponder, the received and transmitted frequencies should be coherent in phase. Traditionally this is done by phase locking the RF carrier at the downlink to that of the uplink. This work introduces a coherent transponder design using Digital Signals Processing (DSP) techniques applied to the baseband part of the coherent transponder to provide a greater flexibility and a higher immunity for space environments. A coherent transponder model was selected. This model consists of three phase locked loops (PLL). The baseband loop has been designed as type digital second order loop. The coherent transponder parameters are calculated based on recommendations of the European Space Agency (ESA). The proposed system was modeled using MATLAB SIMULINK to test its performance like acquisition time and phase error under frequency offset and ramp. The performance parameters in the presence of noise is also tested. A digital Costas loop for demodulating telecommand data was designed and simulated using MATLAB SIMULINK. The performance of the Costas loop to a frequency offset and in the presence of noise is also tested and discussed. The results of the simulated coherent transponder responses are compared with the theoretical calculations and show very close behavior. The results of the simulated digital Costas loop are also very close to the theoretical and the Costas loop gives good performance in the presence of noise.