A magnetic amphidrome is defined as a place where changes of the magnetic field over time, as measured by a total-field magnetometer, are reduced to the point of being negligible. The reduction is caused by destructive interference between the vertical and horizontal components of the time-varying field. At an ideal amphidrome, variations with time are suppressed completely and the total-magnetic-field magnitude is steady. Such a phenomenon may be expected to depend on the frequency content of the time variations in the vertical and horizontal components. The subject is treated first in terms of the quiet daily variation, S q , which is studied on a global basis. It is seen that there are magnetic latitude bands, north and south of the equator, where the quiet daily variation is minimal. These zones are called the "diurnal doldrums." In addition to this global pattern, the magnetic daily variation is modified by Earth's conductivity structure locally, and S q amphidrome behavior may be aided or obstructed locally. The second part of the paper treats the magnetic "rapid fluctuations." A simple condition for an amphidrome is that the direction of Earth's main magnetic field be parallel to the normal of the "preferred plane" in which the small vector changes of rapid magnetic fluctuations tend to lie. Examples are given of observed data for Australia, and a numerical model of Australian electrical-conductivity structure is used to predict amphidromes regionally. Formal treatment of the preferred-plane concept involves taking the out-of-phase (or quadrature) part of the induction phenomenon into account as well, and a parameter is proposed which may be contoured to show an amphidrome minimum. The phenomena of amphidromes are fundamental for magnetic mapping procedures. Near amphidromes, the fluctuating magnetic fields of Earth are suppressed, and their capacity for introducing error into magnetic survey data is reduced correspondingly. The case of a "complete" or "ultimate" amphidrome, applying to both diurnal and rapid fluctuations, may be expected to be rare. None is known at present. The reason is that the diurnal doldrums, favoring, S q amphidromes, occur at low latitudes. Rapid-fluctuation amphidromes, however, are more likely to occur at mid- to high latitudes.