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The problem of the modelling of the strain localisation in elasto-visco-nonlinear materials and structures submitted to so-called "quasistatic" loadings is here considered. Unlike the usual approaches, which suppose that the localisation band remains in (quasi)static equilibrium, it is here assumed that localisation is essentially a dynamic phenomenon, even if the external loadings are "quasistatic". This means that the localisation criterion proposed is also a "local loss of (quasi)staticity" criterion. As soon as the criterion is verified, the dynamic problem is treated (at least locally) instead of the (quasi)static one.