The ALICE experiment at CERN LHC is intensively using a PROOF cluster for fast analysis and reconstruction. The current system (CAF - CERN Analysis Facility) consists of 120 CPU cores and about 45 TB of local space. PROOF enables interactive parallel processing of data distributed on clusters Of computers or multi-core machines. Subsets of selected data are automatically staged onto CAF from the Grid storage systems. However, a cluster of the size of CAF can only hold a fraction of the yearly 3 PB data accumulated by ALICE. The impracticability to store and process such data volume in one single computing centre leads to the need to extend the concept of PROOF to the Grid paradigm.