Bistability due to a second‐order dispersive nonlinearity in a Fabry–Perot resonator is studied. The experiments are performed on a nonlinear transmission line resonator. Nonlinear resonance curves, bistability as well as instabilities, and the generation of harmonics are observed. The theoretical treatment of bistability is based upon a nonlinear dispersion relation as derived from an inspection of two interacting harmonics or, in a second approach, of propagating solitons.