A new type of magnetospheric electrostatic wave, discovered onboard the GEOS 1 satellite, is described. These waves have a wide spectrum, extending between the lower hybrid frequency and the ion plasma frequency. Their main characteristic is their modulation in amplitude at a ULF frequency which is of the order of the helium gyrofrequency. The corresponding electromagnetic ULF waves are detected siultaneously in all cases (26) but one. These ULF-associated electrostatic waves (106) at all geomagnetic latitudes sampled by GEOS 1 (0¿<&lgr;m<+30¿). At least two factors seem to control the existence of these waves: the ULF wave power has to be stronger than 0.02 &ggr;2Hz-1, and the cold plasma density has to be lower than 25 cm-3. Some possible mechanisms for explaining their generation are discussed.