The pseudogap state in the cuprate superconductors shows signs of electronic pair formation above the superconducting temperature. Is it just a ‘precursor’ state or a separate (and competing) state? In fact, both interpretations seem to be correct. The discovery of the pseudogap in the cuprates1,2,3 created significant excitement as it was believed to be a signature of pairing4, in some cases above room temperature. Indeed, a number of experiments detected phase-fluctuating superconductivity above the transition temperature Tc (refs 5, 6, 7 8, 9). However, several recent experiments reported that the pseudogap and superconducting state are characterized by different energy scales10,11,12,13,14, and probably compete with each other15,16, leaving open the question of whether the pseudogap is caused by pair formation. Here we report the discovery of a spectroscopic signature of pair formation and demonstrate that in a region commonly referred to as the pseudogap, two distinct states coexist: one that is due to pair formation and persists to an intermediate temperature Tpair<T* and a second—the ‘proper’ pseudogap—characterized by the loss of spectral weight and anomalies in transport properties that extends up to T*. Tpair has a value around 120–150 K even for materials with very different Tc values and it probably sets a limit on the highest attainable Tc in the cuprates.