The source-time function of megaton class nuclear explosions has been determined by modeling teleseismic short- and long-period body waves with synthetic seismograms. A simple analytic expression for the time function was used to closely match observations from both Novaya Zemlya and the U.S. test site at Amchitka. It was found that the time functions of all the events have a substantial overshoot. It was also found that, although the durations of the time functions did appear to depend on yield, the effect was very difficult to observe even in short-period records. All synthetics were computed by assuming a simple point source in a layered elastic half-space. It was not necessary to appeal to any nonlinear processes in the source region to explain the observations. Numerical calculations are presented to show that tectonic release triggered by earthquakes does not have a substantial effect on the P waves unless the long-period level of the tectonic event is as large or larger than the long-period level of the explosion. The pS wave, on the other hand, is shown to be very sensitive to even a moderate amount of tectonic release.