  We study, by means of an exact analytical solution, the motion of a
spheroidal, axisymmetric squirmer in an unbounded fluid, as well as the low
Reynolds number hydrodynamic flow associated to it. In contrast to the case of
a spherical squirmer --- for which, e.g., the velocity of the squirmer and the
magnitude of the stresslet associated with the flow induced by the squirmer are
respectively determined by the amplitudes of the first two slip ("squirming")
modes --- for the spheroidal squirmer each squirming mode either contributes to
the velocity, or contributes to the stresslet. The results are
straightforwardly extended to the self-phoresis of axisymmetric, spheroidal,
chemically active particles in the case when the phoretic slip approximation
holds.
