Single molecule force clamp experiments are widely used to investigate how enzymes, molecular motors, and other molecular mechanisms work. We developed a dual-trap optical tweezers instrument with real-time (200 kHz update rate) force clamp control that can exert 0–100 pN forces on trapped beads. A model for force clamp experiments in the dumbbell-geometry is presented. We observe good agreement between predicted and observed power spectra of bead position and force fluctuations. The model can be used to predict and optimize the dynamics of real-time force clamp optical tweezers instruments. The results from a proof-of-principle experiment in which lambda exonuclease converts a double-stranded DNA tether, held at constant tension, into its single-stranded form, show that the developed instrument is suitable for experiments in single molecule biology.