Multi-kink solutions of the defocusing, modified Korteweg-de Vries equation (mKdV) found by Grosse [22, 23] are shown to be globally H 1 -stable, and asymptotically stable. Stability in the one-kink case was previously established by Zhidkov [51] and Merle-Vega [41] . The proof uses transformations linking the mKdV equation with focusing, Gardner-like equations, where stability and asymptotic stability in the energy space are known. We generalize our results by considering the existence,

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... ess and the dynamics of generalized multi-kinks of defocusing, non-integrable gKdV equations, showing the inelastic character of the kink-kink collision in some regimes.