FT-Raman and FT-IR spectroscopic techniques have been applied to the study of both the chemical and physical changes that occur in polymers. The vulcanisation process of elastomers was studied, including the formation of sulphur crosslinks, the interactions of the vulcanisation reagents, and the solubility of sulphur in elastomers. Studies were also carried out on the crystallinity of poly(butylene terephthalate). In Chapter 3, FT-IR spectroscopy was used to investigate the interactions of the accelerator and initiator compounds used in the vulcanisation process, in the absence of any elastomer. This led to a structure for the active sulphurating agent being proposed. In Chapter 4, the formation of sulphur crosslinks in ethylene norbornene terpolymer (EPDM) was studied using FT-Raman spectroscopy. The degree of conversion of the reactive sites in EPDM was measured and the presence of crosslinks was observed in the FT-Raman spectra. In Chapter 5, the development of an FT-Raman method to measure the solubility of sulphur in various elastomers is described, and reasons for observed differences in the solubility postulated. In Chapter 6, FT-Raman spectroscopy is used to monitor the cold vulcanisation of rubber using sulphur monochloride. New bands due to the presence of sulphur crosslinks are identified and a direct comparison is made with the observations in Chapter 4 on the accelerated sulphur vulcanised EPDM. In Chapter 7, the development of an FT-IR microscopic method to determine the degree of surface crystallinity of poly(butylene terephthalate) (PBT) is described. Two band measurement techniques are discussed and the results compared with those obtained using differential scanning calorimetry (DSC) measurements.