Dynamic step by step analyses are performed for the study of the structural pounding between a reinforced concrete (RC) frame structure and a steel (ST) frame structure. The examined RC frame is designed to Eurocodes EC2 and EC8 and the ST frame to EC3 and EC8. Both structural systems have ten (10) floor levels. The adjacent structures have non-equal inter-storey height at the base floor and therefore an inter-storey pounding problem takes place. The slabs of the ST structure hit the columns of the RC frame structure and the slabs of the RC frame hit the columns of the ST frame. The seismic response of the structures without the pounding effect is also studied and compared to the corresponding demands that are developed due to the interaction problem. Results in terms of displacements, ductility requirements, flexural demands and shear demands, have shown that in situations where pounding may occur, the potential effects may lead to non-safe building design or evaluation for both structures. Thus, in cases where inter-storey pounding takes place and, especially for the columns of both RC and ST frames that suffer the hit critical increase of the shear and ductility demands, are observed due to the interaction effect.