Structural information on tellurium compounds was obtained from Mössbauer-effect data measured with Te129 sources. The compounds studied were tellurium metal, TeO2, and Te(NO3)4. To check the reliability of the information obtained, experiments were also carried out using Te125 absorbers. It was found that for the tellurium compounds, but not for tellurium metal, the ratio of the quadrupole coupling of the Te129 sources to that of the Te125 absorbers was constant, despite the differences in the ligands and structural properties of these compounds as revealed by differences in their isomer shifts and asymmetry parameters It is concluded that the structure of TeO2 (orthorhombic phase) resembles that of SeO2, namely, a chain structure with three coordinated oxygens and an O-Te-O angle of 90°. From the significant magnitude of the asymmetry parameter, it is concluded that one of the Te-O bonds is longer than the other two. An appreciable anisotropy of the recoilless fraction was found in the case of TeO2 and Te metal, confirming their chain character. For Te(NO3)4, the structure was found to be a tri- or tetrapyramid with the Te atom at the apex, equal Te-NO3 bond distances, and a NO3-Te-NO3 angle close to 90>°. The quadrupole moment of the Te125 first excited state was calculated and found to be -0.19±0.02 b. The energy-level positions in the I129 quadrupole-split spectrum was calculated for intervals of 0.1 in η up to η=1. It is shown that from the greater sensitivity of some transitions to the value of η, it is possible to get quite accurate values of η.