The work presented in this thesis is divided into two chapters, each being devoted to a study of the band system of a diatomic molecule of Group VI elements. The molecules studied were Se₂ and TeO, and their choice depended on the feasibility of the work and on some current trends in theoretical thinking. To gain useful information about these molecules from their spectra it was essential that rotational analyses should be done and thus the experimental work was directed towards achieving high dispersion and maximum resolution, using isotropically pure samples. The theoretical interest in Se₂ and TeO arises from the differences to be found in the molecules formed from the Group VI elements with increasing charge. Thus much of the earlier work on Se₂ has been shown to be wrong because of the misunderstanding of the nature of a ³Σ state for a heavy molecule.