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The motion and evolution of binary tropical cyclones was investigated using a coupled tropical cyclone‐ocean movable nested grid model. The model consists of eight‐layer atmospheric and seven‐layer ocean primitive equation models. Several regimes of binary storm interaction have been identified, depending on the initial separation distance (d) and differences in storm strengths. At d less than a few hundred kilometers, interacting storms experienced complete merger (CM) or partial merger (PM). At larger d (between about 600 km and 1000 km), three regimes of storm interaction have been found: PM, straining out (SO), characterized by complete disintegration of the weaker storm, and mutual straining out (MSO), characterized by weakening and dissipation of both storms. SO occurred when the interacting storms had substantially different intensities and strengths. MSO was observed when the interacting storms were comparable in size and intensity. In the latter case the storms were unable to approach each other at distances smaller than a certain minimum distance (of about 450–500 km) without being mutually stretched out. Moreover, initial attraction of the storms in this regime was replaced by repulsion, as frequently observed in the western Pacific. At d exceeding about 1000 km, elastic interaction (EI) was found, when the storms interact without any significant changes in their intensity and structure. In additional experiments with a conditional instability of the second kind (CISK) type parameterization of convective heating the storm interaction was very different: The storms were nearly axisymmetric and very compact, and they continued approaching each other until they merged. Thus more realistic simulations of binary storm interaction can be achieved by using a physically more reasonable convective parameterization.