We investigate dynamics of a self-propelled deformable particle under
external field in two dimensions based on the model equations for the center of
mass and a tensor variable characterizing deformations. We consider two kinds
of external force. One is a gravitational-like force which enters additively in
the time-evolution equation for the center of mass. The other is an
electric-like force supposing that a dipole moment is induced in the particle.
This force is added to the equation for the deformation tensor. It is shown
that a rich variety of dynamics appears by changing the strength of the forces
and the migration velocity of self-propelled particle
