"Zero-knowledge proofs of membership" are methods for proving that a string x is in a language L without revealing any additional information. This is a fundamental notion that has proven to be useful and applicable in many settings. Two main variants have been considered in the literature. The first, "zero-knowledge proofs of decision power", consists of methods for proving the knowledge of whether a string x is in a language L or not without revealing any additional information. The second, "result- indistinguishable zero-knowledge proofs of decision", consists of methods for transfering whether a string x is in a language L or not without revealing any additional information. Due to the quite stringent definitions of these two variants, it seemed that the class of languages having zero-knowledge proofs of membership was not as large as any of the classes of languages having zero-knowledge protocols in these two models. In this paper we give strong indications that this may not be the case. Our main result is that any language having what we call "meet-the challenge" game as a perfect (statistical) zk proof of membership, has also such a perfect (statistical) zk proof in the two "decision proof" models. This can be extended to prove, among other things, that honest-verifier statistical zk proof of membership for a language implies a honest-verifier statistical zk protocol in the two "decision" models. Technically, we introduce new protocol techniques, such as "language-based coin flipping protocols" that may have other applications.