A new and efficient method for the nonlinear dynamic analysis of steel structures is presented in this paper. The method employs a newly developed quartic formulation which is capable of representing the large displacement behaviour of elastic beam-columns using one element per member. The efficiency of the procedure is further enhanced in the elasto-plastic range through the use of automatic mesh refinement, where the analysis is always started using a coarse mesh to be refined during analysis when and where necessary. Additionally, automatic adjustment of the integration time-step is employed, since such a process is shown to contribute significantly to the efficiency of the nonlinear dynamic analysis of jacket structures. Verification examples using ADAPTIC, a general purpose program for the nonlinear analysis of framed structures subjected to earthquake, blast and impact loads, demonstrate the accuracy and significant computational savings of the proposed analysis method.