The aim of this paper is to introduce and analyze chaotic and hyperchaotic conservative
complex nonlinear systems. These systems appear in several branches of applied sciences.
Lyapunov exponents are calculated to observe chaotic and hyperchaotic behaviors. The wide
range of systems parameters at which chaotic and hyperchaotic solutions exist is calculated. The
modules for complex variables are computed and plotted. The projections of chaotic and hyperchaotic
solutions are shown in 3- spaces and 2-planes. The systems of this paper leave rooms
for further studies in the near future, e.g. control and several types of synchronization of the
solutions of these systems.