Double layers (i.e., electric fields parallel to B) form along auroral field lines in the Earth's magnetosphere. They form in order to maintain current continuity in the ionosphere in the presence of a magnetospheric electric field E with ∇. E ≠ 0. Features which govern the formation of the double layers are: 1) the divergence of E; 2) the conductivity of the ionosphere; and 3) the current-voltage characteristics of auroral magnetic field lines. Astrophysical situations where ∇. E ≠ 0 is applied to a conducting plasma similar to the Earth's ionosphere are potential candidates for the formation of double layers. The region with ∇. E ≠ 0 can be generated within, or along field lines connected to, the conducting plasma. In addition to ∇. E, shear neutral flow in the conducting plasma can also form double layers.