Parametric excitation of surface waves in a magnetic fluid container is investigated under the influence of an externally applied magnetic field. With a view to explain the experimental observation the dynamical equations governing the evolution of the amplitude of instability are obtained using asymptotic methods. The solution of dynamical equations yields a period doubling sequence, orbits of odd periods, and windows of chaos. Also observed is the phenomenon of strange attractor. (C) 1998 American Institute of Physics.