Strongly peaked electrostatic emissions near 10.0 kHz and electromagnetic emissions near 0.56 kHz have been observed by the VLF wave detector on board Imp 6 on crossings from the earth's magnetosphere into the polar cusp during the occurence of large magnetospheric substorms. The electrostatic emissions were observed to be closely confined to the cusp-magnetosphere interface. The electromagnetic emissions were of somewhat broader spatial extent and were seen on higher-latitude field lines within the cusp. Using these plasma wave observations and additional information provided by plasma, magnetometer and particle measurements made simultaneously on Imp 6, theories are constructed to explain each of the two classes of emission. The electromagnetic waves are modeled as whistlers, and the electrostatic waves as electron-cyclotron harmonics. The resulting growth rates predict power spectra similar to those observed for both emission classes. The electrostatic waves may play a significant role via enhanced diffusion in the relaxation of the sharp substorm time cusp-magnetosphere boundary to a more diffuse quiet time boundary.