The -"s" genitives of English and Swedish play an important role in grammaticalization theory, as they are often used as counterexamples to the main tenet of that theory, viz. that grammatical change is unidirectional. In this paper I look at the emergence of the -"s" genitive in Danish, hoping that it may shed some new light on the evolution of -"s" genitives in general, and may provide some evidence for a positive or negative answer to the question whether this evolution is a valid counterexample to the unidirectionality hypothesis. In order to document the history of the Danish "s"-genitive I analyzed the possessive constructions in various versions of one the oldest Danish texts written in Latin script, the provincial law of Jutland ("Jyske Lov"), composed in 1241, but copied by hand until well into the 16th c. In these copies the changes in the language can be followed in detail. The main conclusion of this investigation is that -"s" already had attained its relative autonomy before it was used in group genitives, viz. at the moment when it was glued to the plural forms of nouns, e.g. "maen-s" replacing the old genitive "manna". How this emancipation of -"s" is to be interpreted depends obviously on the status of -"s" as the ending of a certain class of nouns. I argue that the common interpretation of case endings as morphemes should be rejected, they are just the final sounds (Auslaut) of a word. Due to the more than imprecise definition of grammaticalization in terms of movement along a cline, it is not possible to answer the question whether the genesis and evolution of "s"-genitives are a good example of counterdirectional change. (Contains 1 table.)