Cortical neurons show irregular but structured spike trains. This has been interpreted as evidence for 'temporal coding', whereby stimuli are represented by precise spike-timing patterns. Here, we suggest an alternative interpretation based on the older concept of the cell assembly. The dynamic evolution of assembly sequences, which are steered but not deterministically controlled by sensory input, is the proposed substrate of psychological processes beyond simple stimulus-response associations. Accordingly, spike trains show a temporal structure that is stimulus-dependent and more variable than would be predicted by strict sensory control. We propose four signatures of assembly organization that can be experimentally tested. We argue that many observations that have been interpreted as evidence for temporal coding might instead reflect an underlying assembly structure.