We give sufficient and necessary conditions that characterize the existence of an absolutely continuous invariant measure for a degree one $C^2$ endomorphism of the circle which is bimodal, such that all its periodic orbits are repelling, and such that both boundaries of its rotation interval are irrational numbers. Moreover, we prove that those conditions hold for Lebesgue almost every rotation interval. The measure obtained is a global physical measure, and it is hyperbolic. This is a joint work with S. Crovisier and P. Guarino.