Neurons in primary auditory cortex (AI) in the ferret (Mustela putorius) that are well described by their spectrotemporal response field (STRF) are found also to have a distinctive property that we call temporal symmetry. For temporally symmetric neurons, every temporal cross-section of the STRF (impulse response) is given by the same function of time, except for a scaling and a Hilbert rotation. This property held in 85% of neurons (123 out of 145) recorded from awake animals and in 96% of neurons (70 out of 73) recorded from anesthetized animals. This property of temporal symmetry is highly constraining for possible models of functional neural connectivity within and into AI. We find that the simplest models of functional thalamic input, from the ventral medial geniculate body (MGB), into the entry layers of AI are ruled out because they are incompatible with the constraints of the observed temporal symmetry. This is also the case for the simplest models of functional intracortical connectivity. Plausible models that do generate temporal symmetry, from both thalamic and intracortical inputs, are presented. In particular, we propose that two specific characteristics of the thalamocortical interface may be responsible. The first is a temporal mismatch between the fast dynamics of the thalamus and the slow responses of the cortex. The second is that all thalamic inputs into a cortical module (or a cluster of cells) must be restricted to one point of entry (or one cell in the cluster). This latter property implies a lack of correlated horizontal interactions across cortical modules during the STRF measurements. The implications of these insights in the auditory system, and comparisons with similar properties in the visual system, are explored.