Comet P/Grigg-Skjellerup is a comet with a moderate gas production rat
e. Quasi-linear theory, which has successfully described waves upstrea
m of the bow shock of comet P/Halley (a comet with a much higher gas p
roduction rate), is not appropriate in this case. In this paper, we de
velop the nonlinear theory of laminar MHD wave activity upstream of th
e bow shock of P/Grigg-Skjellerup using a combination of analytical an
d numerical methods. The nonlinear saturation mechanism is the trappin
g of cometary ions, resulting in their bounce oscillations over pitch
angle. For the specific case of the Giotto encounter with P/Grigg-Skje
llerup, during which the solar wind propagation was almost transverse
to the magnetic field, the excitation of left-hand circularly polarize
d waves propagating toward the comet is initially dominant. Later on,
as a result of pitch angle scattering of resonant particles, we find t
hat waves propagating toward the Sun are also excited. The numerical s
olutions show that under the action of waves propagating in both direc
tions the cometary ions acquire a spread in energy. The results of thi
s theoretical analysis are compared with measurements made during the
Giotto encounter with P/Grigg-Skjellerup and are found to be in good q
ualitative agreement.