We have modeled central-loop and coincident-loop transient responses of a magnetically viscous layer sandwiched between two nonmagnetic ones. The coincident-loop transients show exponential voltage decrease (at a fixed delay time), at any thickness h2 of the magnetic layer, with an increasing depth to the latter (h1) or the loop height if the layer is exposed on the ground surface. The patterns of central-loop transients are different from those of the coincident-loop ones and from one another for thin and thick magnetic layers. Namely, the voltage first rises to its maximum and then falls as the depth to the magnetic layer (h1) increases, if it is thin: the thinner the layer, the more prominent the peak. If the layer is thick, the voltage decreases monotonically with its depth (or with loop height above the ground). Voltage grows, first rapidly and then progressively more slowly, at ever greater thicknesses of the magnetic layer in both loop configurations. At large h2, the effect from the magnetic layer becomes similar to that from a magnetically viscous halfspace. These features of the transient responses have to be taken into account in planning and conducting TEM surveys, as well as in a geological interpretation of the TEM data affected by natural and/or man-caused magnetically viscous ground. In the general case, the turn-off of the transmitter current induces eddy current in the ground beneath the loop, which decays at a rate proportional to the ground resistivity. The eddy current decay and magnetic relaxation processes being independent at conductivities (resistivities) common to the real subsurface, the effect of the former can be allowed for using the superposition principle. This principle implies that the total response of a magnetically viscous conductor is a sum of the magnetic relaxation and eddy current components.