In order to secure conversationsin Satellite Telecommunications based on GMR-1 standard, the“A5-GMR-1” encryption algorithm is used. The internal structure of this algorithm was not publickly known prior to 2012 and afterward it was revealed by reserve engineering. This thesis introduces A5-GMR-1 encryption algorithmand compares it with A5/2stream cipher algorithm, and tries to provide a security analysis for this algorithm. A common approachtoanalyze any encryption algorithm isto evaluatevarious attacks on it. Due to the structural similarity between A5-GMR-1 and A5/2, and noting that theprevalent attacks against the A5/2, one of the goals of this thesis is to study the feasibilityof Wagner attak against the A5-GMR-1algorithm. In this thesis we prove that this attack is not applicable on A5-GMR-1. As the study of algebraic attack by linearization method and XL algoritm,linearization method is optimized by reducing the space required for the attack. It is shown that theXLmethod hasless memorycomplexity than the optimized linearizationmethod,whereas itscomputationalcomplexity on the attack phase is much higher that the optimized linearization method. Keywords: 1-stream cipher 2-Wagner Attack 3-Algebric Attack 4-linearizatio 5-Xl algorithm