We report on the observation of a nonlinear intensity dependence of the terahertz radiation-induced ratchet effects in bilayer graphene with asymmetric dual-grating gate lateral lattices. These nonlinear ratchet currents are studied in structures of two designs with dual-grating gates fabricated on top of boron nitride encapsulated bilayer graphene and beneath it. The strength and sign of the photocurrent can be controllably varied by changing the bias voltages applied to individual dual-grating subgates and the back gate. The current consists of contributions insensitive to the radiation’s polarization state, defined by the orientation of the radiation electric field vector with respect to the dual-grating gate metal stripes, and the circular ratchet sensitive to the radiation helicity. We show that intense terahertz radiation results in a nonlinear intensity dependence caused by electron gas heating. At room temperature, the ratchet current saturates at high intensities of the order of hundreds to several hundreds of kW cm^-2⁠. At T = 4  K, the nonlinearity manifests itself at intensities that are one or two orders of magnitude lower; moreover, the photoresponse exhibits a complex dependence on the intensity, including a saturation and even a change of sign with increasing intensity. This complexity is attributed to the interplay of the Seebeck ratchet and the dynamic carrier-density redistribution, which feature different intensity dependencies and nonlinear behavior of the sample’s conductivity induced by electron gas heating. The latter is demonstrated by studying the THz photoconductivity. Our study demonstrates that graphene-based asymmetric dual-grating gate devices can be used as terahertz detectors at room temperature over a wide dynamic range, spanning many orders of magnitude of terahertz radiation power. Therefore, their integration together with current-driven read-out electronics is attractive for the operation with high-power pulsed sources.