Operation modes in the system of two mutually synchronized oscillators with both single-ended and double-ended control systems are investigated. The necessary and sufficient conditions for settling common frequency in the system are obtained. It is shown that system in the steady state can be operated in one of several modes. Number of possible modes in the double-ended control system cannot exceed two while in the single-ended control system this number depends on the magnitude of total delay. The necessary and sufficient conditions of existence of separate modes are obtained. The differences between single-ended and double-ended control schemes are pointed out.