alkyl having 1 to 6 carbon atoms, each n is a number such that the hydroxyl equivalent weight is up to 260, x is a number from 1 to 2, R 2 is hydrogen, alkyl having 1 to 6 carbon atoms, or phenyl, o is a number from 1 to 4 and p is 0 or 1. 8. The process of any claims 6 or 7 wherein the final curing step is performed in the presence of no more than 10 ppm of zinc, tin and mercury combined and, except for the alkoxylated Mannich base, no more than 0.05 part by weight of amine group-containing compounds that have molecular weights below 360. 9. The process of any claims 6-8 wherein the final curing step is performed in the presence of no more than 20 ppm of metals and no more than 0.05 weight percent of amine group-containing compounds that have molecular weights of below 350 except for the alkoxylated Mannich base. 10. The process of any of claims 6-9 wherein component a) is reacted with at least a portion of component b-1) to form a prepolymer or quasi- prepolymer having an isocyanate content of 1 to 20 percent by weight and in the final curing step, the prepolymer or quasi-prepolymer is reacted with polyol b-2) and any remaining portion of polyol b-1) at an isocyanate index of 90 to 150 to produce the polyurethane. 11. The process of claim 10 wherein the step of reacting component a) with at least a portion of component b-1) to form a prepolymer or quasi- prepolymer is performed in the presence of no more than 20 ppm of metals and, except for the alkoxylated Mannich base, no more than 0.05 weight percent of amine group-containing compounds that have molecular weights of below 350. 12. The process of any of claims 6-11 wherein component b-1) has a hydroxyl equivalent weight of at least 400. 13. A coating, adhesive, sealant or elastomer comprising the polyurethane polymer of any of claims 1-5. 14. A two-component sealant or adhesive composition comprising