Frequency and width crossing have been observed for two coupled resonances in a microwave cavity. The cavity consisted of two nearly identical rectangular boxes. The boxes were coupled by a slit of variable width. The data are well described by a non-Hermitean S matrix leading to a 2x2 non-Hermitean effective Hamiltonian. The values of the interaction strength |v| for which width crossing and frequency crossing, respectively, were observed, are above and below a critical value |v(c)| for which one expects a joint frequency and width crossing.
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