We demonstrate what is believed to be the first continuous-wave dual-crystal optical parametric oscillator (D-OPO) for generation of waves with a frequency difference of some terahertz. It is based on two magnesium-doped periodically poled lithium niobate crystals pumped with near-infrared light at 1030 nm. By changing the temperature difference of the crystals we achieve a difference-frequency tuning. This ranges from an initially unexpected lower threshold of 1.3 THz up to higher frequencies. The linewidth of the considered signal waves is smaller than 5 GHz. Smaller difference frequencies were not achievable. Our model, describing the dual-crystal parametric gain, explains the observed lower tuning limit by showing that the assumption of independent oscillation conditions in a D-OPO is not necessarily valid.