A method for embolization using liquid embolic materials is described. The method comprises the use of two liquid components. The first liquid component is an aqueous solution or dispersion comprising at least one oxidized polysaccharide. The second liquid component is either an aqueous solution or dispersion comprising at least one water-dispersible, multi-arm amine, or a water-dispersible multi-arm amine in the form of a neat liquid. The two components crosslink in situ to form a hydrogel that should act as an effective embolic agent.