Zermelo's 1929a, the first set-theoretic paper to appear after a break of more than 20 years, is a reaction against criticism of his 1908 notion of definiteness. The paper provoked a swift response by Thoralf Skolem, 1930, a response which had a strong impact on Zermelo's foundational views in the 1930s. In the following we first describe the range and nature of the criticism. We then comment on the paper, and in the concluding section we discuss the impact of Skolem's response.