An optoelectronic self-oscillatory circuit with a constant time delay and its injection locking have been theoretically and experimentally described. The oscillation circuit incorporates a delayed feedback path by utilizing an optical fiber and is characterized by a differential-difference equation. The oscillation waveform and amplitude have been investigated by computing the equation. It is also shown that a stable frequency locking region exists and expands with an increase in the injection amplitude. By employing a carrier signal, two methods for optoelectronic oscillation, an AM and an FM type, are proposed and have been demonstrated to obtain more stable oscillation.