In this thesis both analytical and design studies have been conducted on the behaviour of fully and semi-rigidly connected multistorey steel frames. Many topics have been addressed, current design approaches examined and new design methods proposed to allow for such effects based upon a first order linear elastic analysis, which is the most commonly used in normal design. These topics are as follows: 1) The well known amplified sway method (see BS 5950: 1985: Part 1) which can be used to incorporate the effect of the presence of axial loads on the behaviour of sway frames was studied. A modification to this method has been proposed and the validity of the proposed method was checked using an existing computer program [1] to verify the proposed method against a second order analysis. 2) The influence of the action of semi-rigid connections on frame behaviour was examined and the need to conduct a systematic investigation into the problem verified. A simple hand calculation method to incorporate this influence to any of the conventional design methods has been proposed. A second computer program [2] was slightly modified to suit the university of Sheffield IBM3083 mainframe machine and this program was later used in this study. 3) The stiffening effect due to partial sway bracing resulting from the presence of block or brickwork walls in a practical multistorey frame accompanied by the weakening effect due to the finite stiffness of semi-rigid joints on frame serviceability was investigated and a suitable design method is recommended. 4) The behaviour of columns in sway frames with and without partial sway bracing, resulting from the presence of infill panels in practical frames, has been examined. Design charts which can be used to predict a reasonably conservative estimation of the inelastic ultimate load of a framed column in a sway structure are given. These charts are particularly helpful in assisting a designer to make a reasonably good initial selection for the column section sizes in a flexibly connected frame. In addition an empirical formula has been proposed to incorporate the beneficial effect on the column behaviour resulting from the presence of infill panels in real steel frames. In order to conduct this study a computer program developed by Rifai [3] has been modified to simulate the behaviour of a flexibly connected sway subassemblages. 5) Finally general conclusions and recommendations for future work are given.