  We present an analysis of the dynamics of the M31 satellite system. Proper
motion data exist for only two of the M31 satellites. We account for this
incompleteness in velocity data by a statistical analysis using a combination
of the timing argument and phase-space distribution functions. The bulk of the
M31 satellites are well fit by these models and we offer a table of orbital
properties, including period, eccentricity and semi-major axis. This enables us
to search for evidence of group infall based on orbital similarity rather than
propinquity on the sky. Our results favour an association between Cass II and
NGC 185, as the orbital parameters are in close agreement, but not for NGC 185
and NGC 147, which have often been associated in the past. Other possible
satellite groupings include the pair And I and And XVII; the pair And IX and
And X; and the triple And V, And XXV and NGC 147. And XXII has been claimed as
a satellite of M33; we find that they are not moving independently along the
same orbit, but cannot determine whether they are orbiting each other or are
unrelated. Two satellites, And XII and And XIV, have high line-of-sight
velocities, consistent with very recent infall from the edge of the Local
Group. They are not well described by our underlying smooth phase space
distribution function, and are reanalysed without priors on their orbital
parameters. For And XIV, multiple pericentric passages are possible and
improved distance information is needed to draw further conclusions. For And
XII, orbits which assume at least one pericentric passage can be ruled out and
it must be on its first infall into the M31 system.
