There are two broad exceptions to the general rule that South African courts do not have jurisdiction over offences committed outside South Africa. The first set of exceptions developed by South African courts deals with offences of treason and theft. The second set of exceptions was created by the legislature and includes national and international offences. The prosecution of international offences is based on the principle of universal jurisdiction. This article examines the relevant statutory provisions relating to the offences of torture, terrorism, grave breaches of the Geneva Conventions, war crimes, crimes against humanity and genocide. It will recommend that there is a need for the relevant legislation to be amended to eliminate the ambiguities that relate to the following issues: the place where the suspect has been arrested or found; courts with jurisdiction over the offence and the individual responsible for authorising the prosecution of the offence and designation of the court; the expiry of the right to prosecute; and the prosecution of acts or omissions which took place before the commencement of the Acts.