Method for continuously removing the unreacted butene-1, and optionally other volatile components, from a polymeric solution obtained by liquid phase (co)polymerization of butene-1, the method comprising the steps of: subjecting the polymeric solution to heating and mixing conditions such that a mixture is formed consisting substantially of: (1) a polybutene melt containing entrapped butene-1 and (2) supercritical gaseous butene-1; subjecting the above mixture to a sequence of devolatilization steps operating at decreasing pressures.