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In this paper we analyze mechanisms of coexistence between different cognitive radio systems operating as secondary users in white space frequency bands. In particular, our focus is coexistence mechanisms that can be provided by IEEE 802.19.1 coexistence system. IEEE 802.19.1 standard is at the early stage of its development. At this stage it is very important to consider different design directions and focus areas. This paper presents results of performance evaluation of the IEEE 802.19.1 coexistence system based on simulation. We believe that simulation results shown in this paper and analysis of these results are very important for the future of both IEEE 802.19.1 standard and products based on this standard.