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SNOW 3G is a stream cipher chosen by the 3rd Generation Partnership Project (3GPP) as a crypto-primitive to substitute KASUMI in case its security is compromised. SNOW 2.0 is one of the stream ciphers chosen for the ISO/IEC standard IS 18033-4. In this study, the authors show that the initialisation procedure of the two ciphers admits a sliding property, resulting in several sets of related-key pairs. In case of SNOW 3G, a set of 232 related-key pairs is presented, whereas in the case of SNOW 2.0, several such sets are found, out of which the largest are of size 264 and 2192 for the 128-bit and 256-bit variant of the cipher, respectively. In addition to allowing related-key recovery attacks against SNOW 2.0 with 256-bit keys, the presented properties reveal non-random behaviour that yields related-key distinguishers and also questions the validity of the security proofs of protocols that are based on the assumption that SNOW 3G and SNOW 2.0 behave like perfect random functions of the key-IV.