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Physical layer (PHY) security in decode-and-forward (DF) relay systems is discussed. Based on the types of wiretap links, the secrecy performance of three typical secure DF relay models is analyzed. Different from conventional works in this field, rigorous derivations of the secrecy channel capacity are provided from an information-theoretic perspective. Meanwhile, closed-form expressions are derived to characterize the secrecy outage probability (SOP). For the sake of unveiling more system insights, asymptotic analyses are performed on the SOP for a sufficiently large signal-to-noise ratio (SNR). The analytical results are validated by computer simulations and are in excellent agreement.