This paper deals with the file allocation problem (BFR92) con- cerning the dynamic optimization of communication costs to ac- cess data in a distributed environment. We develop a dynamic file re-allocation strategy that adapts online to a sequence of r ead and write requests whose location and relative frequencies are com- pletely unpredictable. This is achieved by replicating the file in response to read requests and migrating the file in response to write requests while paying the associated communications costs, so as to be closer to processors that access it frequently. We develop first explicit deterministic online strategy assuming existence of global information about the state of the network; previous (deterministic) solutions were non-constructiv e and more expensive. Our solution has (optimal) logarithmic competitive ratio. The paper also contains the first explicit deterministic data migration (BS89) algorithm achieving the best known competitive ratio for this problem. Using somewhat different technique, we also develop the first deterministic distributed file allocation algorithm (using only lo- cal information) with poly-logarithmic competitive ratio against a globally-optimized optimal prescient strategy.