A theory of magnetospheric VLF emission must account for the following features: (a) the triggering of monochromatic emissions by signals of sufficient strength and duration, while the background noise and weak short signals are not amplified, and (b) the occurrence of frequency changes after the emissions have reached a sufficiently large amplitude. A nonlinear mechanism exhibiting these features, with fixed and varying frequencies, is examined analytically and by computer simulation techniques. This mechanism depends on a simultaneous propagation and amplification of wave packets along geomagnetic lines to maintain the nonuniformity ratio R∝∇B0/Bw in the regime ‖R‖≈0.5, corresponding to maximum amplitication. (B0 is the geomagnetic field and Bw is the wave magnetic field.) For a constant frequency, this condition yields triggering thresholds which are related to the properties of the magnetosphere. For a varying frequency &ohgr;(t), it yields the condition ∂&ohgr;/∂t∝&ohgr;2t for the large-amplitude portion of the risers, where &ohgr;t∝B1/2w denotes the trapping frequency of the wave.