We present new distributed algorithms for constructing a Steiner Forest in the congest model. Our deterministic algorithm finds, for any given constant ε > 0, a (2 + ε)approximation inÕ(sk + min {st, n}) rounds, where s is the shortest path diameter, t is the number of terminals, k is the number of terminal components in the input, and n is the number of nodes. Our randomized algorithm finds, with high probability, an O(log n)-approximation in timẽ O(k + min {s, √ n} + D), where D is the

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... ted diameter of the network. We also prove a matching lower bound ofΩ(k + min {s, √ n} + D) on the running time of any distributed approximation algorithm for the Steiner Forest problem. Previous algorithms were randomized, and obtained either an O(log n)-approximation inÕ(sk) time, or an O(1/ε)-approximation inÕ(( √ n + t) 1+ε + D) time.