The influence of Fano resonances on the nonlinear response of hybrid plasmonic nanostructures, i.e., nanoantennas loaded with a nonlinear optical material, is theoretically investigated using the combination of a surface integral equation method and an analytical model. The results demonstrate that a suitable design of the field enhancement enables the observation of optical bistability for incident conditions that would be impossible for a bare nanoantenna. This study provides new insights into the possibilities offered by Fano resonances to control the nonlinear response of hybrid plasmonic systems. (C) 2017 Society of Photo-Optical Instrumentation Engineers (SPIE)