The DC-side line faults in high-voltage direct-current (HVDC) systems utilising voltage-source converters (VSCs) are a major concern for multi-terminal HVDC systems in which complete isolation of the faulted system is not a viable option. A number of challenges are posed by both pole-to-pole and pole-to-ground faults including the presence of very fast and high amplitude discharge current from the DC-link capacitance, the lack of suitable DC current breaking devices, and the lack of highly discriminative fault detection techniques. Therefore, faults occurring along the interconnecting DC cables are likely to threaten system operation. In order to better understand the system under such faults, this paper analyses the behaviour of HVDC systems energised by the conventional two-level VSC. This investigation provides a systematic evaluation of the nature of a DC fault in HVDC systems during a permanent pole- to-pole and pole-to-ground fault taking into consideration a number of influencing parameters including fault position, fault resistance and other operational conditions. To quantify these dependencies on DC voltage and current characteristics a systematic simulation study is undertaken in which the natural responses of the HVDC networks transients during DC side faults are examined. The outcome of this paper lies the necessary knowledge foundation for developing future DC protection methods.