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A spectrum sharing scheme is proposed for overlaid wireless networks based on the decode-and-forward two-path successive relaying technique. In this scheme, two secondary transmitters are used to transmit secondary information alternately to their respective receivers while relaying the primary signal at the same time. The transmission of the primary system is continuous, and the secondary system can opportunistically help the primary transmission in exchange for the spectrum sharing. Superposition coding is used at the secondary transmitters, where the primary signal and secondary signal are linearly combined. Successive interference decoding and cancelation is performed by secondary users to extract their desired signals. For the primary system, joint decoding is performed by treating the secondary signal as noise at the receiver side. The optimal power allocation is determined to maximize the success probability of the secondary system without violating the outage performance of the primary system. Numerical and simulation results show that the proposed scheme can conservatively protect the primary performance while realizing the secondary transmission requirement.