The provision of system-wide heap storage has a number of advantages. However, when the technique is applied to distributed systems automatically recovering inaccessible variables becomes a serious problem. This thesis presents a survey of such garbage collection techniques but finds that no existing algorithm is entirely suitable. A new, general purpose algorithm is developed and presented which allows individual systems to garbage collect largely independently. The effects of these garbage collections are combined, using recursively structured control mechanisms, to achieve garbage collection of the entire heap with the minimum of overheads. Experimental results show that new algorithm recovers most inaccessible variables more quickly than a straightforward garbage collection, giving an improved memory utilisation.