The relationship between individual and collective effects in a two-component plasma is investigated in the case of an unstable equilibrium given by a cold two-stream distribution. The full dynamics of this system is solved using an exact N-body code. As the graininess parameter is large, such a cold plasma should be dominated by individual effects. Indeed, during an initial phase much longer than the plasma period, ions and electrons simply oscillate around each other forming neutral ``molecules". Subsequently, however, the system switches to a regime where collective effects are important: the two-stream configuration becomes unstable and phase space structures appear. On a longer time scale, the streams are destroyed and the system evolves towards thermal equilibrium. The present results show that collective effects can emerge even in a plasma dominated by individual interactions, provided that the initial distribution is unstable.