Transient associations among neurons are thought to underlie memory and behavior. However, little is known about how such associations occur or how they can be identified. Here we recorded ongoing local field potential (LFP) activity at multiple sites within the cortex of awake monkeys and organotypic cultures of cortex. We show that when the composite activity of a local neuronal group exceeds a threshold, its activity pattern, as reflected in the LFP, occurs without distortion at other cortex sites via fast synaptic transmission. These large-amplitude LFPs, which we call coherence potentials, extend up to hundreds of milliseconds and mark periods of loss-less spread of temporal and amplitude information much like action potentials at the single-cell level. However, coherence potentials have an additional degree of freedom in the diversity of their waveforms, which provides a high-dimensional parameter for encoding information and allows identification of particular associations. Such nonlinear behavior is analogous to the spread of ideas and behaviors in social networks.