  We develop a microscopic theory for nonlinear optical response of moir\'e
exciton-polaritons in bilayers of transition metal dichalcogenides (TMDs). Our
theory allows to study the tunnel-coupled intralayer and interlayer excitonic
modes for a wide range of twist angles ($\theta$), external electric field, and
light-matter coupling, providing insights into the hybridization regime
inaccessible before. Specifically, we account for the Umklapp scattering
processes of two exciton-polaritons responsible for enhanced nonlinearity, and
show that it is crucial for describing interactions at strong hybridization. We
reveal a regime of attractive nonlinearity for moir\'e polaritons, stemming
from the anisotropic Coulomb interactions, which can explain some of
experimental features of optical response in TMD bilayers. Furthermore, within
our theory we demonstrate that the attractive nonlinearity can be tuned into
repulsive by applying an external electric field. Our findings show that
nonlinear moir\'e polaritons offer a controllable platform nonlinear
polaritonic devices.
