  We analyze the topological nature of $c=1$ string theory at the self--dual
radius. We find that it admits two distinct topological field theory structures
characterized by two different puncture operators. We show it first in the
unperturbed theory in which the only parameter is the cosmological constant,
then in the presence of any infinitesimal tachyonic perturbation. We also
discuss in detail a Landau--Ginzburg representation of one of the two
topological field theory structures.
