Dealing with convergence in German speech islands in Russia, Brazil and the United states the article discusses the linguistic phenomena related to the notion of convergence from different vantage points including intralinguistic convergence (due to dialect-dialect contact), interlinguistic convergence (due to language-language contact), typological "convergence" (or intralinguistic change), pidginization, and cognitive processes of simplification. Most of the German speech islands are considered to be contracting - if not dying - varieties with respect to the reduction of their grammatical systems. Evidently, for a long time language contact (and sometimes variety contact) have severely increased. Linguistic norms have been weakened in terms of both norm certainty and norm loyalty thus giving way to processes similar to those common to pidgin languages. External induced changes are highly remarkable in all German speech islands. But the susceptibility for change and the ways of change are structured by systematical and typological constraints which probably turn out to be cognitive processes underlying quite "normal" linguistic change. This change is discussed as a subsequent process of "regularization" (of irregular forms), simplification (of rules) and loss of grammatical distinctions (and their compensation). The linguistic description of these interrelated processes is based on an integrated approach providing methodology from sociolinguistics, dialectology and research on language change, including the attempt to highlight the cognitive structures which furrow the line for internal simplifications under external pressure. Comparative speech island research seems to be a promising field of application for the description of the intermesh of these processes.