The contribution presents a set of seismic analyses of multi - storey steel structures with semi-rigid beam column connections acted upon by seismic actions. Semi-rigidity of the structures beam to column connections is conferred by two types of beam to column connections: top and seat and web angle (TSW) and end-plate (EP) joints. Computed numerical results are associated to two classes (static and kinematic) of seismic behaviour parameters expressing the two contradictory effects of semi-rigidity. On one hand, the lateral flexibility induces larger lateral displacements while, on the other hand, it attracts smaller base shear seismic forces. Also, the constitutive relation M − θr induced into semi- rigid beam column connections by seismic actions is presented. The results are presented in their numerical form and in a comparative graphical manner allowing for relevant comments and conclusions