Customary Marriages. In South Africa, the definition of a customary marriage is one that is “negotiated, celebrated or concluded according to any of the systems of indigenous African customary law which exist in South Africa”.This does not include marriages concluded in accordance with Hindu, Muslim or other religious rites.ivil marriages are governed by the Marriage Act and regulations issued in terms of the Act. South Africa also recognizes customary marriages through the Recognition of Customary Marriages Act, which became effective in November 2000.