The intriguing question of the origin of the arm-like magnetic structures seen between the optical spiral arms of certain spiral galaxies is addressed. Using a two-dimensional approximation to the non-linear disc dynamo equation, it is shown that gas streaming along the arms may produce such a field configuration. Another possibility is a spiral modulation of the turbulent diffusivity, associated with an enhancement of turbulence in the interstellar medium within the arms. The effects of a similar modulation of the alpha-effect are also examined. Finally, the consequences of a non-linear feedback of the large-scale field on the turbulent diffusivity ('eta-quenching') are briefly discussed.