This paper shows that the Gerund Phrase (GP) in the Spanish Gerund Construction (e.g., El jefe entró a su oficina corriendo, lit. The boss entered his office running ) is sometimes a complement (in SGCC) and sometimes an adjunct (in SGCA). Although in both cases, the GP expresses a non-argument of the main lexical verb's denotation, it is a syntactic adjunct in SGCA and a syntactic dependent of the main clause s head in SGCC. We argue that there is a semantic correlate of this syntactic difference and propose a general principle that constrains the semantic relations that can hold between the denotata of heads and added members of their ARG-ST lists: The two denotata must be part of a larger macro-event in the sense of Talmy (2000). We further show that the relation between the events denoted by the gerund and main verbs involves four semantic conditions and that which subset of those four conditions are satisfied in a particular SGCC sentence determines what subkind of SGCC is involved.