Trivium is a stream cipher candidate of the eStream project. It has successfully moved into phase three of the selection process under the hardware category. No attacks faster than the exhaustive search have yet been reported on Trivium. Bivium-A and Bivium-B are simplified versions of Trivium that are built on the same design principles but with two registers. The simplified design is useful in investigating Trivium-like ciphers with a reduced complexity and provides insight into effective attacks which could be extended to Trivium. The Bivium ciphers have been previously cryptanalysed. This talk focuses on a guess and determine attack method based on a satisfiability problem in propositional logic. Using a minimal amount of keystream we can recover the internal state and obtain the private key.