Summary: Phase-locked solutions of coupled oscillators are studied with asymmetric coupling strengths and inhomogeneous natural frequencies. The solutions exhibit profiles of phase lags resulting from the pacemaker corresponding to the ratio of upward and downward coupling strengths. Using the existence condition for phase-locked solutions, the transition points from phase-locked to phase-drift states are evaluated. The application of existence condition to the case of linear gradient of natural frequency illustrates some scaling properties in frequency diagrams.