Research in damage detection and structural health monitoring in engineering systems during their service life has received increasing attention because of its importance and benefits in maintenance and rehabilitation of structure. Though the concept of vibration-based damage detection has been in existence for decades, and several procedures have been proposed to date, its practical applications remain limited, considering the increased utilization of sensors to measure structural response at multiple points. In this thesis, use of acceleration response of the structure as a method of global damage detection is explored using instantaneous frequency and stiffness degradation methods. Instantaneous frequency was estimated using continuous wavelet transform of measured acceleration response of the structure subjected to ground motion. Complex Morlet Wavelet was used in the time-frequency analysis due to its ability to provide sufficient resolution in both time and frequency domains. This ability is important in analyzing nonstationary signals like earthquake response of structure containing sharp changes in the signal. The second method, called the stiffness degradation analysis, is based on estimating the time-varying stiffness. This estimation is done by fitting a moving least-square line to the force-displacement loop for the duration of the ground motion.A four-story shear building is used as the model structure for numerical analysis. Two damage scenarios are considered: single damage instant and multiple damage instants. Both scenarios assume that the damage occurs at a single location. In the numerical simulations, damage was modeled as a reduction in the stiffness of the first floor, and accelerations were computed at floor levels using state-space model. The two methods were compared in terms of their damage detection ability and it was shown that both methods can be used in detecting damage and the time at which the damage occurs. These methods can later be extended by simultaneously considering the correlations of responses at all floor levels. This extension may enable locating the damage and quantifying the severity of the damage.