We report on transient-pulse nonlinear spectroscopy with the radiation of a multimode THz gas laser. The method is demonstrated for studying the nonlinear response of a current-carrying superlattice to THz radiation; the current through a superlattice can be suppressed by a strong THz field. The method makes use of the pulses of a high power multimode THz gas laser. By splitting the laser beam for selected laser modes into a main beam and a reference beam we monitored with a reference detector the transient power in the main beam. The simultaneous measurement of both the instantaneous response and the instantaneous power allows to obtain the power dependence of the response within a single laser pulse. The method is suitable to study the nonlinear response of matter to THz radiation fields in a large dynamic range.