The dynamic performance of railway bridges is an increasingly relevant issue in public transport systems due to the extensive construction of new High-Speed railway lines and the use of old lines for higher operating train velocities. Higher design velocities may lead to resonant phenomena, entailing adverse consequences such as ballast destabilization, risk of derailment, deterioration of passenger comfort and a raise in the maintenance costs, especially in short simply supported structures. In order to mitigate the excessive vertical oscillations experimented by bridge decks, a specific type of retrofit is proposed. It consists on artificially increasing the overall damping, retrofitting the deck with fluid viscous dampers linking the vertical motion of the slab with that of an auxiliary structure. This solution could substitute a classical strengthening process in existing railway bridges, being one of its principal advantages the possibility of installation and maintenance without interfering with everyday railway traffic. The research line has evolved in order to fulfil two main objectives: (i) assessing the technical feasibility of the proposed alternative and, (ii) developing a design methodology for the dampers and auxiliary structure based on the overall damping level needed to achieve an admissible dynamic performance of the superstructure. A finite element code has been implemented specifically to predict the retrofitted structure response under railway traffic. This code constitutes the main numerical tool of analysis. As short simply supported bridges are commonly built by means of pre-stressed concrete slabs, T-beam decks, slabs stiffened with ribs etc. the bridge deck is modelled as an orthotropic thin plate simply supported on elastic bearings. On the other hand the combined structure is analysed under harmonic simplified conditions, and closed form expressions for the retrofitting system parameters are formulated following a three-dimensional analytical approach. The adequacy of these expressions is validated through extensive numerical analyses. In all the cases evaluated, the retrofitted bridge dynamic response reduces to acceptable levels without exceeding the dampers axial force capacity, the maximum admissible stress in the auxiliary structure or the bearable punching load in the slab. Finally two real bridges belonging to the Spanish railway network are analyzed. In each case the bridge model is calibrated in order to accurately reproduce experimental measurements from static and dynamic tests performed on the structures in the past. A hypothetic increase in the respective lines operating velocity is considered leading to excessive vertical accelerations at the deck platform. A particular retrofit is proposed for each structure and the dynamic responses of the bare and retrofitted structures are compared. The controlling effect of the retrofitting system and the applicability of the optimal parameters analytical expressions are proven for a wide range of trains and circulating velocities. In order to realistically assess the technical feasibility and effectiveness of the proposed solution, special attention has been given throughout the Thesis to several practical aspects related to the auxiliary structure and dampers installation.