Integration in the head-direction system is a computation by which horizontal angular head velocity signals from the vestibular nuclei are integrated to yield a neural representation of head direction. In the thalamus, the postsubiculum and the mammillary nuclei, the head-direction representation has the form of a place code: neurons have a preferred head direction in which their firing is maximal [Blair and Sharp, 1995, Blair et al., 1998, ?]. Integration is a difficult computation, given that head-velocities can vary over a large range. Previous models of the head-direction system relied on the assumption that the integration is achieved in a firing-rate-based attractor network with a ring structure. In order to correctly integrate head-velocity signals during high-speed head rotations, very fast synaptic dynamics had to be assumed. Here we address the question whether integration in the head-direction system is possible with slow synapses, for example excitatory NMDA and inhibitory GABA(B) type synapses. For neural networks with such slow synapses, rate-based dynamics are a good approximation of spiking neurons [Ermentrout, 1994]. We find that correct integration during high-speed head rotations imposes strong constraints on possible network architectures.