The invention relates to polymers derived at least from one: (A) one N-vinyl amide unit, and (B) one hydroxyl-containing acrylate unit, and to polymers derived at least from: (A) N-vinyl-2-caprolactam, and (B) one non-acrylate unit having: (i) at least one hydroxyl group, and/or (ii) at least one functional group convertible to a hydroxyl group wherein at least one group is converted to hydroxyl functionality in the final polymer product. Such polymers may exhibit degradability, e.g., in seawater or soil environments. In preferred embodiments, these polymers and compositions thereof are used in oilfield applications, such as an inhibitor of gas hydrates and/or a kinetic inhibitor of gas hydrates. The polymer can assume alternating, block, and/or random configurations of the repeating units, with at least one ester group. The chemical structure subscripts m, and n may be any integer equal to or greater than 1.