The recent fabrication of thin-film helicoidal bianisotropic mediums (HBMs) has created an impetus for understanding their electromagnetic response. Using the Oseen transformation, we have derived a 4×4 matrix ordinary differential equation for oblique (i.e. non–axial) propagation in general linear HBMs. A perturbational technique is presented for almost-axial propagation; and two other techniques—one semi–analytic and the other analytic—are presented for general oblique propagation. All three techniques yield exact closed-form results for axial propagation. Our use of the Oseen transformation amounts to viewing oblique propagation not by itself but as a graft on axial propagation, and is thus responsible for the stability of all three techniques.