A process for reducing the restart pressure of streams selected from waxy crude oils, water-in-crude emulsions and dispersions of hydrocarbon hydrates, at least partially structured. A mechanic disturbance is applied, in flow-stop conditions, on the streams, having: temperatures lower than the WAT (Wax Appearance Temperature) for the waxy crude oils and water-in-crude emulsions; temperatures lower than the forming temperatures of the hydrates and pressures higher than the forming pressure of the hydrates, for the dispersions of hydrocarbon hydrates.