This paper updates a previously described analytical approach (1,2) using computer technology to investigate the time-dependent material non-linear behaviour of two dimensional moment-frame, truss-frame, and braced-frame steel structures during significant excursions into the post-elastic range. The approach includes considerations for energy analysis; element buckling; stable or unstable mechanism formation; yield capacity reduction resulting from interaction of axial load and bending moment; stiffness degradation; P-δ effects; viscous damping; joint panel zone deformation; and also incorporates a suitable element load-deformation relationship. The computer program NLDYN2 which incorporates this approach has been implemented successfully on many steel structures ranging from 60-story moment frames to braced frames having aspect ratios of up to 10.