The study of chaotic complex nonlinear systems has become a subject of great ?interest during the last 30 years. The aim of this thesis is to introduce and study ?some chaotic complex nonlinear dynamical systems, for example, complex ?Chen and Lü systems?. There are interesting cases of dynamical systems, where the main variables ?participating in the dynamics are complex, for example, when amplitudes of ?electromagnetic fields of laser systems are involved. Another example is when ?chaos synchronization is used for communications, where doubling the number ?of variables may be used to increase the content and security of the transmitted ?information.? This monograph is mainly addressed to graduate students and senior ?researchers interested in the study of complex nonlinear systems.?