Two terminal electrical measurements of freestanding multiwalled carbon nanotubes employing tunnelling contacts have been made. Previous electrical characterisation on both single and multiwalled carbon nanotubes have revealed a zero bias anomaly, in which the current is characterised by a power law (I ∝ Va+1). In the case of single wall nanotubes this behaviour has been explained within Luttinger liquid theory, the strong repulsive electron-electron interactions found in one dimension causing Fermi liquid theory to break down. The origin of the power law in the characteristics of multiwalled nanotubes is less clear and is the subject of considerable debate. In part, the debate is fuelled by the very similar predictions of the various theories, particularly those of Luttinger liquid and single junction Coulomb blockade theory. The measurements presented in this thesis employ a unique combination of a freestanding geometry with high resistance tunnelling contacts, which are necessary to probe electron-electron interactions. The results are quantitatively very different to all previous reports and are explained using the environmental quantum fluctuations found in single junction Coulomb blockade. The size of the quantum fluctuations is strongly influenced by the high frequency impedance of the nanotube. The freestanding geometry causes reflections within the nanotube, resulting in an impedance-frequency characteristic significantly different to that expected for conventional on-substrate geometries. It is proposed that this is the cause of the large quantitative difference between the results gained from the freestanding geometry and the on-substrate geometry. The exponent, a which characterises the power law (I ∝ Va+1) is typically around 0.3 in the conventional on-substrate geometries (both theoretically and experimentally). The original results presented in this thesis show a ~ 3.5 and the exponent shows considerable variation. The non-conventional freestanding geometry, splits for the first time, the predicted exponent from Luttinger liquid and environmental quantum fluctuations theories as they are applied to multiwalled carbon nanotubes. The later interpretation is favoured not only because of the quantitative agreement with the exponent, a but unlike Luttinger liquid theory it is also in agreement with other experimental observations, such as offset ohmic behaviour. The agreement is such that these results could be the best demonstration of environmental quantum fluctuations in a single junction Coulomb blockade. The power law in MWNTs appears to have several manifestations. Uniting them all in a single explanation could well be impossible. So, while this work may not end the debate on the origin of the power law in MWNTs it certainly will make a significant contribution.