We develop a hydrodynamic model for the calculation of sum and difference frequency generation ͑SFG/DFG͒ at the surface of nonlocal conductors with arbitrary equilibrium electronic density profiles n 0 . We apply our model to simple profiles and calculate the nonlinear surface susceptibility tensor zzz s ( 1 , 2 ) and the radiated efficiency R( 3 ϭ 1 Ϯ 2 ) as a function of the pump frequencies 1 and 2 . R is strongly enhanced due to the excitation of the dipolar surface plasmon characterized by a resonant frequency d ; it displays ridges whenever 1 , 2 , or 3 Ϸ d , an additional ridge at the bulk plasma frequency 3 Ϸ b , and very large double resonance peaks whenever two ridges cross each other. These results suggest that SFG/DFG spectroscopy might be a useful probe of surface collective modes.