The oblique propagation problem in a dielectric thin-film helicoidal bianisotropic medium (TFHBM), which has a reference uniaxial basis and exhibits second-harmonic generation (SHG), is solved. First, the linear constitutive relation is set up, followed by a constitutive relation to describe SHG. Then, a homogeneous 4 × 4 matrix ordinary differential equation is solved for the linear electromagnetic field phasors, and an inhomogeneous 4 × 4 matrix ordinary differential equation is solved for the second-harmonic electromagnetic field phasors. Extension to more general nonlinear HBMs shall follow the same route, provided the angular frequency of the nonlinear field generated is different from the angular frequencies of the linear fields that are needed to generate the nonlinear field. © 1996 John Wiley & Sons, Inc.