We propose multidimensional timestamp protocols for concurrency control in database systems where each transaction is assigned a timestamp vector containing multiple elements. The timestamp vectors for two transactions can be equal if timestamp elements are assigned the same values. The serializability order among the transactions is determined by a topological sort of the corresponding timestamp vectors. The timestamp in our protocols is assigned dynamically and is not just based on the starting/finishing time as in conservative and optimistic timestamp methods. The concurrency control can be enforced based on more precise dependency information derived dynamically from the operations of the transactions. Several classes of logs have been identified based on the degree of concurrency or the number of logs accepted by a concurrency controller. The class recognized by our protocols is within D-serializable (DSR), and is different from all previously known classes such as two phase locking (2PL), strictly serializable (SSR), timestamp ordering (TO), which have been defined in literature. The protocols have been analyzed to study the complexity of recognition of logs. We briefly discuss the implementation of the concurrency control algorithm for the new class, and give a timestamp vector processing mechanism. The extension of the protocols for nested transaction and distributed database models has also been included.