We introduce a model of temporal evolution of political opinions which amounts to a dynamical extension of Galam model in which the proportions of inflexibles are treated as dynamical variables. We find that the critical value of inflexibles in the original Galam model now turns into a fixed point of the system whose stability controls the phase trajectory of the political opinions. The appearance of two phases is found, in which majority-preserving and regime-changing limit cycles are respectively dominant, and the phase transition between them is observed.