Magnetic fields with translational symmetry, axisymmetry, and helical
symmetry are integrable. That is, they have good flux surfaces. The cu
rrent closure condition, that phidl/B is a flux surface quantity, also
holds. It is possible to construct magnetic fields with broken symmet
ry, which have nearly integrable magnetic fields. It is shown that for
nearly integrable nonsymmetric fields, the current closure condition
need not hold.