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We apply a recently developed approximation method to two standard models for orientation tuning: a one-layer model with difference-of-Gaussians connectivity and a two-layer excitatoryinhibitory network. Both models reveal identical steady states and instabilities to high firing rates. The two-field model can also loose stability through a Hopf-bifurcation that results in rhythmically modulated tuning widths around 0 to 50Hz. The network behavior is almost independent of the relative weights and widths of the kernels from excitatory to inhibitory cells and back. Formulas for tuning properties, instabilities, and oscillation frequencies are given.