To provide a complex damper having high impact or vibration energy absorbing capability while reducing ill effects on environment without using lead, and to provide a base isolating structure equipped therewith having sufficient base isolating performance and damping performance.

The complex damper 15 comprises a complex of wire rods 16 selected from metal wires, organic fibers and inorganic fibers and a soft and flexible plastic 17 containing the wire rod 16. The wire rods are aligned with each other perpendicular to the direction of shearing deformation. The base isolating structure comprises a laminate having rigid hard plates 12 and rubber layers 13 alternately laminated and the damper 15 provided in a hollow portion 14 bored in the laminating direction of the laminate.