In this paper, we describe a dynamic causal model (DCM) of steady-state responses in electrophysiological data that are summarised in terms of their cross-spectral density. These spectral data-features are generated by a biologically plausible, neural-mass model of coupled electromagnetic sources; where each source comprises three sub-populations. Under linearity and stationarity assumptions, the model's biophysical parameters (e.g., post-synaptic receptor density and time constants) prescribe the cross-spectral density of responses measured directly (e.g., local field potentials) or indirectly through some lead-field (e.g., electroencephalographic and magnetoencephalographic data). Inversion of the ensuing DCM provides conditional probabilities on the synaptic parameters of intrinsic and extrinsic connections in the underlying neuronal network. This means we can make inferences about synaptic physiology, as well as changes induced by pharmacological or behavioural manipulations, using the cross-spectral density of invasive or non-invasive electrophysiological recordings. In this paper, we focus on the form of the model, its inversion and validation using synthetic and real data. We conclude with an illustrative application to multi-channel local field potential data acquired during a learning experiment in mice.