A family of keystream generators, called the LILI keystream generators, is proposed for use in stream cipher applications and the security of these generators is investigated with respect to currently known attacks. The design is simple and scalable, based on two binary linear feedback shift registers combined in a simple way, using both irregular clocking and nonlinear functions. The design provides the basic security requirements such as a long period and high linear complexity, and is resistant to known cryptanalytic attacks.