  (abridged) We want to provide further evidence of the origin of the proposed
stellar members of Chamaeleon and to identify interlopers from the foreground
\epsilon Cha and \eta Cha associations. To this aim, we compile lists of
spectroscopically confirmed members of Chamaeleon I and II, \epsilon Cha and
\eta Cha, and of background objects in the same line of sight. Using Virtual
Observatory tools, we cross-match these lists with the UCAC3 catalogue to get
the proper motions of the objects. In the vector point diagram, we identify the
different moving groups, and use this information to study the membership of
proposed candidate members of the associations from the literature. For those
objects with available radial velocities, we compute their Galactic space
velocities. We look for correlations between the known properties of the
objects and their proper motions. The members of the dark clouds exhibit
clearly different proper motions from those of the foreground associations and
of the background stars. The data suggest that Chamaeleon II could have
different dynamical properties from Chamaeleon I. Although the two foreground
clusters \epsilon and \eta Chamaeleontis constitute two different proper motion
groups, they have similar spatial motions, which are different from the spatial
motion of Chamaeleon I. On the other hand, the space motions of the Chamaeleon
II stars look more similar to those of the foreground clusters than to the
Chamaeleon I stars, but the numbers are low. Hence, with the available data it
is unclear to what extent the stellar populations in both clouds are physically
connected to each other. We find no correlations between the proper motions and
the properties of the objects in either of the clouds.
