Damping arrangement for low, medium and high-rise structures (1) using bidirectional damping means (5) such as visco-elastic Gensui damping devices, placed between two parallel elements of the structure (1), such as a core (2) and a perimeter column (3), or between two cores. Oscillatory or other flexural or shear deformations of the structure (1) are damped by damping axial movements between the two elements (2, 3), and simultaneously damping orthogonal movements between the two elements (2, 3). Outriggers (6, 7, 8) are used to enhance the axial damping moment, and the bidirectional damping means (5) may be installed in pairs, working in opposition to each other to damp dynamic shear or flexural forces in the orthogonal plane.