  In this note we analyse two different models of two interacting conformal
Carroll particles that can be obtained as the Carrollian limit of two
relativistic conformal particles. The first model describes particles with zero
velocity and exhibits infinite dimensional symmetries which are reminiscent of
the BMS symmetries. A second model of interaction of Carrollian particles is
proposed, where the particles have non zero velocity and therefore, as a
consequence of the limit c to 0, are tachyons. Infinite dimensional symmetries
are present also in this model.
