A new and simple time domain approach for the design of first order and second order stabilizers for a single-machine infinite-bus system is presented in thls paper. The poles of the stabilizer a r e pre-specified and the remaining design freedom in the stabilizer is utilized t o assign two eigenvalues corresponding t o the mechanical modes of the system exactly t o the desired locations. In the case of second order stabilizer, the additional design freedom available is used t o shift the unassigned eigenvalues of the system t o a stable region, thus guaranteeing stability of the closed-loop system during the design stage itself. A numerical example is worked out t o illustrate the effectiveness of the proposed design.