From experimental researches and analytical studies, it has been fully proven that the resistance and stiffness parameters of elements and structures decline during cyclic loading due to the dynamic nature of seismic excitations. The simultaneous effect of the magnitude of the system response and the number of loading cycles is expressed by cumulative damage laws; In other words, the current deformation of an element or structure depends on the accumulation of damage in all past oscillations that remain in the system's memory. The analysis and design of structures based on performance and the branch of health monitoring of structures has led to having a clear picture of the amount of possible damage at different levels of risk, and in the last few decades, it has drawn the attention of many researchers to this field by developing different evaluation methods. In this research, the evaluation of the cumulative damage of steel structures under far and near field earthquakes has been investigated using Park-Ang and Kratzig damage indices. Two structural systems of special steel moment frame and dual structural system (special steel moment frame and special concentric braced frame) with the number of floors 8, 15 and 23 were studied and investigated. The results of this research show that the Kratzig damage index shows more damage values than the Park-Ang damage index for the same structure under the same earthquake record, and the damage values are reduced by changing the moment frame system to a dual structural system.