Abstract: This is part 2 of the series "A generalization of the adelic analysis theory of Tate and Iwasawa to arithmetic surfaces"

Abelian extensions of a two-dimensional local field can be described by open subgroups of the topological Milnor K₂-group of the field. Abelian extensions of the field of rational functions of an arithmetic surface can be described using a Milnor K₂-deles which generalize the K₁-group of adeles in dimension one, and its appropriate quotients. The K₁-groups of the two adelic spaces on the arithmetic surface are related via the K₂-delic groups.