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In this paper, we investigate some cross-layer cooperative strategies for cognitive Time-Division Multiple-Access relay channels with bursty arrivals. The proposed schemes adopt an advanced physical (PHY) layer cooperation and an “intelligent” cognitive network-layer cooperation in order to improve the stable throughput region of the system. In contrast to previously reported work, where relaying is only enabled on periods of source silence, here, we incorporate a Dynamic Decode-and-Forward (DDF) policy which allows relaying assistance also during the source transmission. The enhancement of cognitive relaying with DDF provides more cooperative opportunities which results in faster emptying of the user queues and higher stable throughput compared to the conventional approaches. In addition to this PHY-layer relaying, the cognitive cooperation is supported by an adaptive/non-adaptive superposition scheme which allows the relay node to simultaneously forward packets from different users. We demonstrate that superposition can further increase the transmission opportunities and significantly improve the stable throughput region. The proposed schemes are studied from a networking perspective and their advantages are shown through both theoretical results and computer simulations.