This paper is for practical reasons divided into two parts: the present part I, containing sections 1.-6.4., and the concluding part II (to appear in the following issue of this journal), containing sections 6.5.-6.8. The paper is a rather detailed discussion of Hjelmslev’s Outline, mainly from the standpoint of the phonology of Danish (not so much from a theoretical linguistic point of view). After an introduction (1.), including a comparison between the descriptive method used in the Outline and generative phonology (1.1.), the “categories of constituents” are discussed (3.), especially the status of i and u (3.1.). Within the consonantal system (4.), the main interest is devoted to the reductions of ?p It ?k (4.1.1.), and of ?ð and ?γ (4.1.2.), and the reduction of consonants into glossemes is criticized (4.2.). Within the vowel system (5.), attention is paid to the reduction of ?æ (5.1.1.) and to vowel quantity (5.1.3.). In section 6. the location of the stød (6.2.), the cenematy boundary (6.3.), and the syllable boundary (6.4.) are discussed. The examination of Hjelmslev’s stød-rules (6.5.) includes a discussion of “stød-basis” (22.214.171.124.). The imperatives are considered in 6.6., and Diderichsen’s criticism of the Outline is mentioned in 6.7.