This paper presents structural condition assessment of some critical neoclassical monuments in Nepal using nonparametric and parametric system identification techniques. Neoclassical buildings in Nepal house critical administrative units. Structural condition assessment of such buildings is therefore important for the safety of their occupants and interrupted function during and after major earthquakes. The historical and cultural values of such monuments necessitate regular structural assessment for maintenance, repair, and preservation. Dynamic characteristics such as natural vibration frequencies of structures provide valuable insights on their structural condition. While numerical models are commonly used to estimate eigen frequencies of structures, they are associated with large uncertainties in massive monuments with complex structural and geometrical configurations. Noninvasive dynamic identification techniques provide an alternative means in such structures. Ambient vibration records from six neoclassical monuments in the Kathmandu Valley, Nepal are used in this study to estimate vibration frequencies of the structures in different states. The structures were damaged during the 2015 Gorkha earthquake, and subsequently retrofitted. Changes in vibration frequencies before and after retrofitting provide useful insights on structural improvement through retrofitting. Input-output and output-only system identification techniques are tested to simplify the structural condition assessment approach. We conclude that the state space system identification can stably quantify dynamic properties so stiffness variation can be confidently extracted, which is the key application for noninvasive structural system identification. Also, using minimum number of sensors, we captured damage aggravation deploying the modal assurance criterion. The outcomes indicate that structural condition assessment of complex structures is possible using a limited number of sensors for circumstances such as damage aggravation to temporal variation (evolution/reduction) of dynamic characteristics.