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 f/sub /spl lscr// send and receive link failures (with f/sub /spl lscr///sup a/ 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 /spl ges/ 4f/sub /spl lscr// + 2ff/sub /spl lscr///sup a/+ 3f/sub a/ + 1 processes for coping with f/sub a/ Byzantine faulty processes. The probability of disagreement after R iterations is only 2/sup -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.