In recent years, various aspects of human life have been influenced by information technology. Consequently the importance of information tramission security has been increased. Thus, the need for efficient cryptograghy algorithms that can satisfy specific requirements and stand against attacks, is felt much more than the past. Among these, stream ciphers, because of high speed and simple implementation, have many applications in cryptosystems and so their efficiency and security improvement are always under the consideration. It is clear that the investigation of different attacks is necessary for security analysis of cryptosystems. In this thesis, after the introduction of stream ciphers and important attacks against them, we emphasize on algebraic attack which is basically solving nonlinear equations of the stream ciphers algorithms. Then a new method is proposed for counting the number of extra equations in relinearization method. Therefore algebraic attack is considered against regular clocking systems. After this, we consider algebraic attack against systems with memory and this attack is employed against BSRA systems. Finally, this attack is considered for clock-controlled cipher systems and new algebraic attacks are proposed against A5 systems.