We present a set of global, self-consistent N-body/SPH simulations of the dynamic evolution of galactic discs with gas and including magnetic fields. We have implemented a description to follow the ideal induction equation in the SPH part of the code Vine. Results from a direct implementation of the field equations are compared to a representation by Euler potentials, which pose a ∇ ċ B-free description, a constraint not fulfilled for the direct implementation. All simulations are compared to an implementation of magnetic fields in the code Gadget. Starting with a homogeneous field we find a tight connection of the magnetic field structure to the density pattern of the galaxy in our simulations, with the magnetic field lines being aligned with the developing spiral pattern of the gas. Our simulations clearly show the importance of non-axisymmetry of the dynamic pattern for the evolution of the magnetic field.