Complex-fractional systems are systems that are governed by a differential equation characterized by complex order fractional derivatives. A new modeling tool is proposed and used to study these systems: complex order state-space representation. The tool results from the extension of the differentiation order, from order 1 to complex order, in the state equation of classical state-space representation: A modal decomposition of complex-fractional systems and an analytical expression of their output are given. A stability condition is then established. Finally, an academic example illustrates results.