The Thesis presents an in-depth study of arcing behaviour of H. B. C. Fuses for a range of fuse elements and fillers, under critical current conditions. The methodologies used were the standard breaking capacity short-circuit test plus the application of crow-bar, Xray studies, metallographic microscopic and optical fiber arc detection techniques. Due to the observation of some unknown and puzzling arc phenomena it was decided to pursue the arc investigation by an extensive test programme of single uniform wire fuse elements. From the investigation a basic arc mechanism for the pre-peak and post-peak arcs period was discovered. The new mechanism was applied to single wire, strip, long notched, medium notched and short notched fuse elements and to paralleled wires and strips immersed in three quartz filler types: standard sand, high quality granular quartz and bound quartz in two different sizes. The proposed arc mechanism was modelled by a computer program which was used to simulate the described fuse constructions. The results of over 800 tests and subsequent simulation undoubtedly confirm that the proposed arc mechanism is applicable for the described fuse types. The experimental and analytical results are close enough to justify the model application for fuse designers and fuse users. A critical comparison of the experimental and analytical results with previous findings published by other researchers is presented. A detailed arc mechanism and the key behaviour rules are proposed, they are: " Maximum column voltage can not exceed the arc-root voltage. " The arc-root voltage and the initial dv/dt values are influenced by filler characteristics and are able to precisely characterize the filler behaviour. " The dv/dt, and consequently the burn-back are instantaneous current density functions. The application of the above rules allows the fuse designer to tailor the fuse element in order to obtain specific current and arc voltage waveforms. It is believed that the proposed arc mechanism and computer model is able to explain some puzzling are phenomena and eventually could be applied to predicting other low overload H. B. C. fuse behaviour.