Flow constrictions occur when canals or rivers are subjected to a reduction in width because of natural constraints (e.g. debris accumulations, longitudinal bars, confluences) or hydraulic works (e.g. bridge embankments, guide banks, spur dikes). This paper aims to provide new insights on the temporal evolution of the bed profiles at and downstream of river contractions based on special experiments at laboratory scale. In a previous experimental campaign at University of Basilicata, Italy, several runs were performed under steady flow and clear-water scour conditions. In this study new experiments are presented under unsteady flow conditions. Six experiments were carried out considering stepped hydrographs of different shapes. Laboratory tests were performed in a 20 m long straight channel having a rectangular cross section 1.0 m wide and 1.0 m deep. The working section was made by almost uniform coarse sand. The contraction model was 1.0 m long and the contraction ratio (i.e. the ratio of the width of the uniformly contracted area to the width of the undisturbed channel) equal to 0.80. The experiments were performed under clear-water scour regime also for the peak discharges. Starting from novel empirical formulas related to steady flow conditions, an approach is proposed for the prediction over time and along the channel centreline of the maximum (contraction) scour depth, the scour hole length, and the bed profile. Comparison between observed data and predicted values reveals a satisfactory agreement. The relationships here introduced appear to be suitable for practical purposes.