A polyisocyanate composition, suitable for use in the production of elastomers by the RIM process, said composition being the product of reacting an alcohol and/or thiol having an average hydroxyl and/or thiol functionality of from about 1.5 to about 4 and an average hydroxyl and/or thiol equivalent weight of at least 500 with at least 2 equivalents, per hydroxyl and/or thiol equivalent, of an organic polyisocyanate under such conditions that at least about 20 % of the initially formed urethane and/or thiourethane groups are converted to allophanate and/or thioallophanate groups.