It is well known the low capacity of unreinforced masonry (URM) buildings to withstand seismic excitations, thus, many reinforcement techniques (tie rods, buttresses, collar beams, etc.) have been developed, aiming at improving their dynamic response. Such techniques increase the strength and sometimes the ductility of the structural members.  However, in the last two decades, vibration control techniques have been tested and applied as an alternative to reduce the seismic response of URM buildings. These techniques, based on performance approaches, rely on the dissipation of kinematic energy by placing passive devices able to add damping into the structure. Among them, viscoelastic (VE) devices can supply self-centering capacity and dissipate energy through the shear deformation of viscoelastic layers. In contrast with other dampers, VE devices can have linear behavior which simplifies their design and application to URM structures. This paper presents the results of a parametric analysis comparing the dynamic response of a URM building strengthened with a traditional technique and with VE devices. A FEM model was generated using a prototype based on viceregal buildings (18^th century) located in Mexico. Limit states for damage were defined based on the literature and the response was evaluated in terms of displacements (drifts) and energy.