In this study, a systematic investigation is carried out on the seismic behaviour of plane moment resisting steel frames (MRF) to repeated strong ground motions. Such a sequence of earthquakes results in a significant damage accumulation in a structure because any rehabilitation action between any two successive seismic motions cannot be practically materialised due to lack of time. In this work, thirty-six MRF which have been designed for seismic and vertical loads according to European codes are first subjected to five real seismic sequences which are recorded at the same station, in the same direction and in a short period of time, up to three days. Furthermore, the examined frames are also subjected to sixty artificial seismic sequences. This investigation shows that the sequences of ground motions have a significant effect on the response and, hence, on the design of MRF. Additionally, it is concluded that ductility demands, behaviour factor and seismic damage of the repeated ground motions can be satisfactorily estimated using appropriate combinations of the corresponding demands of single ground motions.