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In distributed system, deadlock is a common phenomenon. If a transaction requires more than one resource for its task to be accomplished, such request is called an AND model request. In this paper we have proposed a method for elimination of AND model deadlocks in distributed system. A Multi Granular Locking (MGL) technique is proposed which locks the database at various granules. This technique is used to find the status of the resource which a particular transaction is requesting and protects the database from conflicting access with some preconditions posed for the new transaction.