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In the last several years, Twitter is being adopted by the companies as an alternative platform to interact with the customers to address their concerns. With the abundance of such unconventional conversation resources, push for developing effective virtual agents is more than ever. To address this challenge, a better understanding of such customer service conversations is required. Lately, there have been several works proposing a novel taxonomy for fine-grained dialogue acts as well as develop algorithms for automatic detection of these acts. The outcomes of these works are providing stepping stones for the ultimate goal of building efficient and effective virtual agents. But none of these works consider handling the notion of negation into the proposed algorithms. In this work, we developed an SVM-based dialogue acts prediction algorithm for Twitter customer service conversations where negation handling is an integral part of the end-to-end solution. For negation handling, we propose several efficient heuristics as well as adopt recent state-of- art third party machine learning based solutions. Empirically we show model's performance gain while handling negation compared to when we don't. Our experiments show that for the informal text such as tweets, the heuristic-based approach is more effective.