Modern orb-weaving spiders have evolved well-designed adhesives to capture preys. This adhesive is laid on a pair of axial silk fibres as micron-sized glue droplets that are composed of an aqueous coat of salts surrounding nodules made of glycoproteins. In this study, we measure the adhesive forces required to separate a small microscopic probe after bringing it in contact with a single glue droplet. These forces are highly rate-dependent and are two orders of magnitude higher than the capillary forces. The glycoproteins in the glue droplets behave as a viscoelastic solid and the elasticity is critical in enhancing adhesion caused by specific adhesive ligands. These results have important implications in mimicking bioadhesives.