The main purpose of this paper is to determine the dynamic characteristics and the structural stability of the two approach viaducts of the Bosphorus Suspension Bridge under the expected stresses that would be caused during earthquake conditions. The Ortakoy and the Beylerbeyi approach viaducts constitute the side spans of the bridge at two locations. The bridge's main span over the Bosphorus is suspended, whereas they are supported at the base at either end. For the numerical investigation of the viaducts, 3-D computational structural finite element-FE models were developed. Their natural frequencies and the corresponding mode shapes were obtained, analyzed, presented and compared. The performances of the viaducts, under earthquake conditions, were studied considering the P-Delta effects implementing the push-over (POA) and the non-linear time-history analyses (NTHA). For the NTHA, three earthquake ground motions were generated depending on the location of the bridge. Seismic performances of the viaducts were determined in accordance with the requirements of the Turkish Seismic Code for the Earthquake Design of Railways Bridges (TSC-R/2008) and those of Caltrans (CALTRANS-2001) given for Seismic Design of Steel Bridges, separately. Furthermore, the investigation was extended for evaluating the possible need for retrofitting in the future. After the analysis of the resultant data, a retrofit recommendation for the viaducts was presented.