Transverse magnetic pulsations polarized in the east-west direction (toroidal waves) are a common feature in the dayside magnetosphere, but they are also observed in the nightside magnetosphere in the form of transient oscillations typically lasting 10--20 min. Until now, little attention has been paid to these transient toroidal waves (TTWs). To get insight into the propagation mode and generation mechanism of TTWs, we have examined magnetic field records from the elliptically orbiting AMPTE CCE, geostationary GOES 5 (located at a geographic longitude of ~75 ¿W), and GOES 6 (~100 ¿W) satellites. We find that TTW onset times are often simultaneous among the satellites within an accuracy of 1--2 min, but that the wave periods differ from one satellite to another. The latter feature is evidence that TTWs are due to standing Alfv¿n waves on individual magnetic field lines. Additional evidence of the standing waves is provided from the phase relationship between oscillations in magnetic field and ion flux anisotropy. We show by a numerical calculation of the ionospheric damping rate that toroidal mode standing waves can last for a few wave periods once they are excited. Thus, the general lack of continuous toroidal waves on the nightside can be attributed to the absence of sources rather than to strong ionospheric damping. Using CCE data and ground magnetic field data, we confirm that TTWs can be observed immediately following ~30% (~2%) of substorm onsets when the satellite is on the nightside (dayside) at 4<L<7. Substorms and pseudo substorm onsets produce magnetohydrodynamic disturbances in the near-Earth magnetotail, and these disturbances appear to be a major source of TTWs. ¿ American Geophysical Union 1996