  We investigate the stability of strings connecting charges Q in the
representation {2Q+1} of SU(2) Yang-Mills theory in (2+1) dimensions. While the
fundamental {2}-string between two charges Q=1/2 is unbreakable and stable, the
string connecting static charges transforming under any other representation
Q>1/2 is unstable and decays. A charge Q=1 can be completely screened by gluons
and so the adjoint {3}-string ultimately breaks. A charge Q=3/2 can be only
partially screened to a fundamental charge Q=1/2. Thus, stretching a {4}-string
beyond a critical length, it decays into the stable {2}-string by gluon pair
creation. The complete breaking of a {5}-string happens in two steps, it first
decays into a {3}-string and then breaks completely. A phenomenological
constituent gluon model provides a good quantitative description of the energy
of the screened charges at the ends of an unstable string.
