The behaviour of the interfacial surface tension of nematics near the nematic-isotropic phase transition has been investigated by several researchers. However, the observations reported by the various authors appear to be inconsistent. The present work is an attempt to identify the causes of such inconsistencies. A detailed study of the behaviour of the interfacial surface tension of 5CB by two different techniques (pendant drop and sessile drop) as well as optical observations of the surface of the drop near the nematic-isotropic transitions is presented. Our observations would indicate that close to the transition the phase at the surface may not be uniform; some areas on the surface appear to be fluctuating between the isotropic and the nematic phase. These fluctuations occur at temperatures corresponding to the range between the spinodal points.