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We introduce a novel hybrid failure model, which facilitates an accurate and detailed analysis of round-based synchronous, partially synchronous and asynchronous distributed algorithms under both process and link failures. Granting every process in the system up to fℓ send and receive link failures (with fℓa arbitrary faulty ones among those) in every round, without being considered faulty, we show that the well-known randomized Byzantine agreement algorithm of (Srikanth & Toueg 1987) needs just n ≥ 4fℓ + 2ffℓa+ 3fa + 1 processes for coping with fa Byzantine faulty processes. The probability of disagreement after R iterations is only 2-R, which is the same as in the FLP model and thus much smaller than the lower bound 0(1/R) known for synchronous systems with lossy links. Moreover, we show that 2-stubborn links are sufficient for this algorithm. Hence, contrasting widespread belief, a perfect communications subsystem is not required for efficiently solving randomized Byzantine agreement.