The damage occurred during recent earthquakes in many existing reinforced concrete (r.c.) buildings designed before the introduction of modern anti-seismic codes has shown that these structures are very vulnerable to the seismic action due to their reduced ductility capacity. Therefore, the assessment and reduction of the seismic vulnerability of these systems is a task of extreme importance and passive control systems have proven to be very efficient devices for the seismic retrofit of existing r.c. frames. However the introduction of a bracing into a low ductility frame usually induces remarkable changes both in the collapse modalities and in the probabilistic properties of the seismic behaviour of the structure and this aspect assumes a considerable importance in consequence of the high degree of uncertainty affecting the seismic input. In this paper, the authors consider the case of r.c. frames with limited ductility whose seismic performance is enhanced by adding, within its bays, a system of diagonal dissipative braces with elasto-plastic behavior. The dissipative braces are designed following an often employed design method involving the pushover analysis of the bare frame and for different levels of the target shear capacity assigned to the bracing system. The probabilistic seismic response and vulnerability of the structure is investigated by building, for all the analyzed cases, fragility curves of the system and of its most vulnerable components.