Abstract Nuclear magnetic resonance of 125Te has been observed at 1.3 K in rapidly solidified specimens of Te and TeSe alloys, which were prepared by casting a quartz ampoule containing the melt into ice water. The NMR in rapidly solidified Te is different from the one observed in single-crystal or polycrystalline Te, and it consists of a sharp and isotropic resonance line along with a broad background. When the rapidly solidified Te is annealed, the sharp and isotropic line disappears and the resonance line of polycrystalline Te is observed. It has been concluded from the results of X-ray experiments as well as NMR experiments that there exists a non-crystalline part in rapidly solidified Te before annealing. It has been considered that the non-crystalline Te consists of a number of small spiral chains and that the sharp and isotropic line and the broad background observed in the NMR of rapidly solidified Te come from the atoms at the ends of the small chains and those in the chains, respectively. It is estimated from the ratio of the magnitude of the sharp line to that of the broad background that the small spiral chains in non-crystalline Te consist of about ten atoms.