In this paper we investigate the extent to which the properties of the waves observed at comet Halley during the Giotto encounter can be understood within the context of linearized Vlasov theory. In the region that is magnetically connected to the comet, fluctuations in the plasma frame of reference are detected near 4 and 10 mHz, close to the water cyclotron frequency, as well as at 20--60 mHz, which is well above the water cyclotron frequency. Using a variety of approximations for the ion distribution function, we show that waves having properties similar to those observed can then be generated with appropriate choices of plasma parameters. In the region that is magnetically disconnected from the comet, distinct peaks are observed in the magnetic power spectrum at 7, 21, 29, and 35 mHz, with a hint of a peak at 14 mHz. We show that an anisotropic distribution of pickup water group ions is able to generate unstable waves at as many as 6 harmonics in wave number in the observed range of frequencies. When Doppler shifted into the frame of the Giotto spacecraft, these harmonics in wave number will be observed as harmonics of the water ion cyclotron frequency. ¿ American Geophysical Union 1990