A clamp system for attaching accessory devices to a railing structure includes a first clamping jaw member and a second clamping jaw member designed to clamp on a railing structure. An accessory mounting device includes a cylindrical collar portion with a plurality of diametrically aligned holes arranged around the circumference. One of the clamping jaw members has an opening, sized to receive the collar portion and one pair of holes that can be aligned with the holes of the collar portion. When the mounting device is in a desired orientation, a pin is inserted through the aligned holes to hold the orientation. A locking nut is mounted on a threaded portion of the collar portion and, when tightened, tends to withdraw the collar portion against the pin, firmly securing the assembly together.