The influence of structural overstrength on the seismic behaviour of steel structures and on the assessment of the q factor has been studied by means of a suitable procedure, based on the selection of a significant set of homogeneous historical earthquakes and on the statistical analysis of the dynamic inelastic response of the structure to these accelerograms. Six schemes of steel frames, proportioned according to different design criteria and therefore with different amounts and distribution of overstrength, have been analysed. Three values of the behaviour factor have been considered for each one. The large number of results, obtained by more than 4800 dynamic analyses, has been elaborated in a statistical way, providing damage level indexes which express the probability of yielding and collapse and the plastic level reached, both for the single section and the whole frame. Interesting conclusions have been obtained. In particular, the effectiveness of the capacity design criteria in reducing the probability of collapse of frames has been highlighted. Similar good results have been obtained even when the same overstrength is given to all columns, without any particular attention to its distribution, while the increment of the beam resistance was not favourable in any case. Moreover, a very large improvement in safety has been obtained with just a little increase in the column strength over that supplied by the application of the capacity design criterion. The global behaviour appears thus connected to a new parameter, herein defined and named “effective behaviour factor”, which takes into account the mean overstrength both of beams and columns