Nonlinear equations of the Kadomtsev-Petviashvili type are derived for Alfv¿n and magnetosonic waves propagating at a small angle to the Earth's magnetic field. This represents a generalization of the derivative nonlinear Schr¿dinger equation to the two-dimensional case. The theory is applied to explain the observations of stable Alfv¿n-like solitons by means of the Aureol 3 satellite during the Russian seismic impact experiments. It may also be useful for theoretical interpretations of the chevron structures of the ''pearls'' that are occasionally observed in the Earth's magnetosphere. ¿ American Geophysical Union 1996