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IP routers use lookup tables to forward packets. They also classify packets to determine which flow they belong to in order to decide the type of quality of service they should receive. Increasing the rate of communication links and expansion of the global network is in contrast with the practical processing power of the switching devices. We propose a neural network scheme for the IP lookup problem. Our algorithm-a 12 layers neural network-represents acceptable results on the error rate and training time. Fortunately, parallel processing of neural networks provides a huge processing power to process packets. Our algorithm can be implemented in hardware on a single chip and can perform an IP lookup in only 4.5 nanoseconds implying it can support 60 Gbps link rate. Pipelining and parallel processing can be used to increase the link rate up to 400 Gbps and decrease the learning time.