We investigate theoretically and experimentally the computational properties of an optoelectronic neuromorphic processor based on a complex nonlinear dynamics. This neuromorphic approach is based on a new paradigm of or reservoir computing, which is intrinsically different from the concept of Turing machines. It essentially consists in expanding the input information to be processed into a higher dimensional phase space, through the nonlinear transient response of a complex dynamics excited by the input information. The computed output is then extracted via a linear separation of the transient trajectory in the complex phase space, performed through a learning phase consisting of the resolution of a regression problem. We here investigate an architecture for photonic neuromorphic computing via these complex nonlinear dynamical transients. A versatile photonic nonlinear transient computer based on a multiple-delay is reported. Its hybrid analogue and digital architecture allows for an easy reconfiguration, and for direct implementation of in-line processing. Its computational efficiency in parameter space is also analyzed, and the computational performance of this system is successfully evaluated on a standard spoken digit recognition task. We then discuss the pathways that can lead to its effective integration.