The bursting disc assembly has a primary bursting disc (10) and a secondary bursting disc (20) immediately behind and supporting the primary bursting disc. Each of the said discs (10,20) is made of metal and is gas impermeable, and the bursting strength of the assembly is derived from both of the bursting discs acting in combination. The primary and secondary bursting discs are in contact over the whole of the operating area of the disc, and are shaped together as a pair. The materials of the two discs can be chosen suitably for their functions. The primary disc is for example corrosion-resistant.