From a geophysical point of view, curvelets can be seen as the representation of local plane waves. They can be useful for a series of seismic processing tasks. Here we propose to use the decomposition in the curvelet domain in the context of velocity model scanning for prestack time migration. We start from an initial prestack time migration that we decompose into curvelet components. Each individual component is kinematically demigrated and then remigrated in a new velocity model. The demigration/migration sequence is reduced to a simple mapping of the curvelet coefficients and avoids the classical summations along isochrones. An application on a 2D real data set shows the advantages and the current limitations of the time demigration/migration approach.