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The need for automatic object and event detection systems is increasing everyday, with the large number of surveillance cameras deployed in public environments. Recognition and classification of human activities are important parts of intelligent surveillance systems. In this paper, we dealt with the problem of classification of walking and running which are two important human activities. To solve this problem we used dynamic information of rectangular boxes that surround the subject of interest. In order to demonstrate the effectiveness of this approach, the system is trained and tested on a set of walking and running people videos. In our experiments, we achieved 3% classification error rate using period-based features and a neural network classifier. These results show that our method is able to overcome many challenges such as variations in people's physical attributes, colour of clothing and style of motion.