In a diagnostic system, a diagnostic unit for an operator of an electronic endoscope and a diagnostic unit for an instructor are in half-duplex radio communication. An inquiry that is input as a voice signal through a microphone into the electronic endoscope is superimposed on a modulated picture signal while shifting the phase of the voice signal, to produce an RF signal, which is sent as an electric wave to an operator's processor and an instructor's processor. The processors demodulate the RF signal, to display an endoscopic image based on the picture signal and output the inquiry through speakers based on the voice signal. An instruction that is input as a voice signal through a microphone into the instructor's processor is superimposed on a dummy signal, to produce an RF signal, which is sent as an electric wave to the operator's processor, to output the instruction through the speaker.