  We study the Kowalevski expansions near singularities of the swinging
Atwood's machine. We show that there is a infinite number of mass ratios $M/m$
where such expansions exist with the maximal number of arbitrary constants.
These expansions are of the so--called weak Painlev\'e type. However, in view
of these expansions, it is not possible to distinguish between integrable and
non integrable cases.
