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Proximity based services are location based services (LBS) in which the service adaptation depends on the comparison between a given threshold value and the distance between a user and other (possibly moving) entities. While privacy preservation in LBS has lately received much attention, very limited work has been done on privacy-aware proximity based services. This paper describes the main privacy threats that the usage of these services can lead to, and proposes original privacy preservation techniques offering different trade-offs between quality of service and privacy preservation. The properties of the proposed algorithms are formally proved, and an extensive experimental work illustrates the practicality of the approach.