The study of rhythmic activity in various areas of the brain has been the object of many experimental and theoretical investigations. This talk concerns the generation of rhythmic mixed-mode oscillations (a temporal pattern consisting of a combination of subthreshold oscillations and spikes) at theta frequencies (4-12 Hz), and the transition from theta to "epileptic" activity in a biophysical model of medial entorhinal cortex stellate cells (SCs). This model consist of a multiscale, high-dimensional system of nonlinear ordinary differential equations describing the evolution of voltage and other biophysical variables. During the interspike interval, where subthreshold oscillations are generated, the SC model can be reduced to a three-dimensional fast- slow system. Voltage is the fast variable and the two slow variables are the two components (fast and slow) of the hyperpolarization- activated (h-) current. Using dynamical systems arguments we provide a mechanism for the generation of subthreshold oscillations and the onset of spikes. This mechanism is based on the three-dimensional canard phenomenon. We show that, in this biophysical SC model, the subthreshold oscillatory phenomenon is intrinsically nonlinear and three dimensional, involving the participation of both components of the h-current. We invoke similar dynamic arguments to explain the transition from theta to epileptic activity in networks of stellate cells connected through synaptic excitation. Under these conditions, SCs synchronize. We show that their firing frequency depends on the maximal synaptic conductivity. This coupling parameter has a threshold value above which the SC firing frequency jumps from theta values to a much higher frequency. We demonstrate that this behevior depends on the dynamic nature of excitation, and cannot be achieved by increasing the tonic (constant) drive to the coupled SCs. Consistently with experimental results, we also show that by increasing synaptic inhibition to the coupled SCs their firing frequency returns the the theta regime.