A Displacement-Based Design (D.B.D.) procedure is adopted for the retrofit of framed structures by inserting hysteretic damped braces (HYDBs) in order to attain, for a specific level of seismic intensity, a designated performance level. To check the reliability of the design procedure, two six-storey buildings are considered as having steel and r.c. framed structures, which, originally designed in a medium-risk seismic region, have to be retrofitted as if in a high-risk seismic region. To avoid high deformability of the steel structure at the damage limit state (SLD) and brittle behaviour of the r.c. structure at the life-safety limit state (SLV), two retrofitting structural solutions are examined: additional diagonal braces; HYDs supported by the additional diagonal braces. Nonlinear dynamic analyses under real ground motions are carried out by a step-by-step procedure. The frame members and the HYDs are idealized by a bilinear model; an elastic behaviour is considered for the braces.