One remarkable difference between European and Brazilian Portuguese is related with the setting of the Null Subject Parameter (NSP). While European Portuguese (EP) behaves like a prototypical romance null subject language, contemporary Brazilian Portuguese (BP) is a partially pro-drop system (Duarte 1995; Kato 2000), with preferably overt referential subjects and null expletive subjects in finite clauses, a procedure consistent with a discourse orientation shown by BP (Kato and Duarte 2003). The aim of this paper is to show that the subject position of non-finite clauses begins to show some “side effects” or “by-products” of the ongoing process of change. Our analysis will compare the position of arbitrary subjects of infinitival sentences in EP and BP inspired by the diachronic analysis of Cavalcante (2006) of such structures in Classical Portuguese (from the 16th to the 18th century) and Modern European Portuguese (19th century). According to Cavalcante’s analysis, the use of impersonal clitic SE in variation with a null arbitrary subject in infinitival sentences declines from 20% in Classical Portuguese to 10% in Modern European Portuguese. The examples below illustrate the possible representations of the arbitrary “external argument” of the infinitive: EXAMPLE (1a-c) (1a) illustrates the empty subject; in (1b), the clitic SE could be interpreted as a nominative SE and in (1c), as a passive SE, since the inflected infinitive agrees with the internal argument of abreviar (to shorten). In each case, however, the external argument is suspended and has arbitrary interpretation. The same patterns can be found with tough-movement constructions. In this paper we compare contemporary Brazilian and European Portuguese, using samples from speech and writing. The results for the speech samples reveal that (a) EP exhibits the same pattern observed in the 19th century data (an average of 8% of clitic se); (b) BP, on the other hand, shows an increasing tendency to use overt subjects, specially the nominative pronoun você (you) in variation with impersonal clitic SE, some of the strategies used for arbitrary reference in finite clauses (Kato & Tarallo 1986; Duarte, Barbosa & Kato 2001 among others), a clear evidence of the embedding of the process of change in progress: EXAMPLE (2) As for the written language, a more similar behavior is found for both varieties. Since Brazilian traditional grammars have been built according to the 19th century EP, the rates of clitic SE are close to the ones found for Modern and Contemporary EP and the use of nominative pronouns is extremely rare. A qualitative analysis of se-constructions shows, however, that in EP, the clitic assures an arbitrary reading of the infinitival subject; in BP, on the other hand, such a constraint does not apply.