  Recently, a topological proof of the spin-statistics Theorem has been
proposed for a system of point particles which does not require relativity or
field theory, but assumes the existence of antiparticles. We extend this proof
to a system of string loops in three space dimensions and show that by assuming
the existence of antistring loops, one can prove a spin-statistics theorem for
these string loops. According to this theorem, all unparametrized strings(such
as flux tubes in superconductors and cosmic strings ) should be quantized as
bosons. Also, as in the point particle case, we find that the theorem excludes
nonabelian statistics.
