The invention relates to a method for producing polymers, particularly polyhydroxyurethanes (PHU) from alkenyl ether polyols or pre-polymers that contain monomer units derived from such alkenyl ether polyols, and polythiol compounds, as well as to a method for crosslinking compounds containing alkenyl ether groups, with polythiol compounds. The invention also relates to the polymers and crosslinked polymers that can be obtained using the method according to the invention.