We present the first experimental investigation of the real-time dynamics of predissociation in a diatomic molecule involving more than two electronic states - the predissociation of the D(1)Pi(u) state of Rb-2. Our results show that the state is strongly predissociated, tau approximate to 5 ps, above a sharp energy threshold. We propose that mainly the (1)(3)Delta(u) state causes the fast predissociation and that the fine-structure components of the products are mixed by coupling among molecular states at large internuclear distances. Furthermore, an outward-inward asymmetry of the wavepacket signal is attributed to autoionisation of the wavepacket evolving in the probe (Rydberg) state.