  We extend strong/weak coupling duality to string theories without spacetime
supersymmetry, and focus on the case of the unique ten-dimensional,
nonsupersymmetric, tachyon-free $SO(16)\times SO(16)$ heterotic string. We
construct a tachyon-free heterotic string model that interpolates smoothly
between this string and the ten-dimensional supersymmetric $SO(32)$ heterotic
string, and we construct a dual for this interpolating model. We find that the
perturbative massless states of our dual theories precisely match within a
certain range of the interpolation. Further evidence for this proposed duality
comes from a calculation of the one-loop cosmological constant in both
theories, as well as the presence of a soliton in the dual theory. This is
therefore the first known duality relation between nonsupersymmetric
tachyon-free string theories. Using this duality, we then investigate the
perturbative and nonperturbative stability of the $SO(16)\times SO(16)$ string,
and present a conjecture concerning its ultimate fate.
