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The phenomenon of hysteresis is commonly observed in many UV thermal experiments involving unmodified or modified nucleic acids. In presence of hysteresis, the thermal curves are irreversible and demand a significant effort to produce the reaction-specific kinetic and thermodynamic parameters. In this article, we describe a unified statistical procedure to analyze such thermal curves. Our method applies to experiments with intramolecular as well as intermolecular reactions. More specifically, the proposed method allows one to handle the thermal curves for the formation of duplexes, triplexes, and various quadruplexes in exactly the same way. The proposed method uses a local polynomial regression for finding the smoothed thermal curves and calculating their slopes. This method is more flexible and easy to implement than the least squares polynomial smoothing which is currently almost universally used for such purposes. Full analyses of the curves including computation of kinetic and thermodynamic parameters can be done using freely available statistical software. In the end, we illustrate our method by analyzing irreversible curves encountered in the formations of a G-quadruplex and an LNA-modified parallel duplex.