Comet P/Grigg-Skjellerup is a comet with a moderate gas production rate. Quasi-linear theory, which has successfully described waves upstream of the bow shock of comet P/Halley (a comet with a much higher gas production rate), is not appropriate in this case. In this paper, we develop the nonlinear theory of laminar MHD wave activity upstream of the bow shock of P/Grigg-Skjellerup using a combination of analytical and numerical methods. The nonlinear saturation mechanism is the trapping of cometary ions, resulting in their bounce oscillations over pitch angle. For the specific case of the Giotto encounter with P/Grigg-Skjellerup, during which the solar wind propagation was almost transverse to the magnetic field, the excitation of left-hand circularly polarized waves propagating toward the comet is initially dominant. Later on, as a result of pitch angle scattering of resonant particles, we find that waves propagating toward the Sun are also excited. The numerical solutions show that under the action of waves propagating in both directions the cometary ions acquire a spread in energy. the results of this theoretical analysis are compared with measurements made during the Giotto encounter with P/Grigg-Skjellerup and are found to be in good qualitative agreement. ¿ American Geophysical Union 1995