Both the supersymmetric SO(32) and E 8 × E 8 heterotic strings in ten dimensions have known strong-coupling duals. However, it has not been known whether there also exist strong-coupling duals for the non-supersymmetric heterotic strings in ten dimensions. In this paper, we construct explicit open-string duals for the circle-compactifications of several of these non-supersymmetric theories, among them the tachyon-free SO(16) × SO(16) string. Our method involves the construction of heterotic and open-string interpolating models that continuously connect non-supersymmetric strings to supersymmetric strings. We find that our non-supersymmetric dual theories have exactly the same massless spectra as their heterotic counterparts within a certain range of our interpolations. We also develop a novel method for analyzing the solitons of non-supersymmetric open-string theories, and find that the solitons of our dual theories also agree with their heterotic counterparts. These are therefore the first known examples of strong/weak coupling duality relations between nonsupersymmetric, tachyon-free string theories. Finally, the existence of these strong-coupling duals allows us to examine the non-perturbative stability of these strings, and we propose a phase diagram for the behavior of these strings as a function of coupling and radius* Throughout this paper, we shall use the phrase "Type I" to indicate the general class of openstring theories, regardless of whether they have spacetime supersymmetry. Similarly, we shall use the phrase "Type II" to signify closed strings with left-and right-moving worldsheet supersymmetry, regardless of whether they have spacetime supersymmetry. These terms will therefore be used in the same way as the general term "heterotic". * Note, in particular, that we are only algebraically rewriting the loop amplitude, not constructing to the tree amplitude, and consequently we may simply define t ′ = 1/t as a convenient variable and do not require the tree variable ℓ = 1/8t.