The paper examines some aspects of language contact in the regions of present-day Azerbaijan focusing on the Southeast Caucasian language Udi and its ancestor (Caucasian Albanian). Both languages are marked for a rather pronounced impact from languages that must have played a dominant role since Classical antiquity and in Medieval times. Here, at least three layers can easily be isolated: (a) Old Armenian, (b) both Northwest Iranian and Southwest Iranian, (c) Turkic in terms of Oghuz Turkic (Azeri). Both (Early) Modern Persian and Azeri conditioned that Udi was later-on at least partly integrated into the world of Oriental language despite of the fact that its speakers remained Christians. The pre-Oriental impact from Armenian and (mainly northwest) Iranian languages resulted in significant shifts with respect to both the lexicon and the grammar of Caucasian Albanian and Udi that set apart both languages from the world of Lezgian languages. The paper illustrates the presence of different Iranian layers in Caucasian Albanian and Udi, addressing both lexical and morphosyntactic issues. With respect to morphosyntax, two topics are discussed, namely the emergence of Split-O strategies in Caucasian Albanian and Udi and the development of a system of floating agreement clitics. Both patterns represent instances of structural borrowings from local Iranian languages, which likewise testifies the former relevance of Iranian languages in Central Azerbaijan.