  Using the theory of fibre bundles, we provide several equivalent intrinsic
descriptions for the Hilbert spaces of $n$ ``free'' nonrelativistic and
relativistic plektons in two space dimensions. These spaces carry a ray
representation of the Galilei group and a unitary representation of the
Poincar\'{e} group respectively. In the relativistic case we also discuss the
situation where the braid group is replaced by the ribbon braid group.
