This study investigates the acquisition of A- and A'-bound pronouns by children acquiring English and Brazilian Portuguese as their native languages. It is observed that children performed at chance level when resumptive pronouns placed in extractable positions were tested. Children also behaved at chance level when pronouns locally A-bound by both referential and quantified antecedents were tested. These results diverge from the results reported in Chien and Wexler (1990) and Thornton and Wexler (1999). It is claimed that the difference in experimental results is due to an experimental artifact present in these studies. An account is offered based on the assumption that bound pronouns are elsewhere elements (Hornstein (2001)). Their use requires computation that is claimed to be beyond children's limited working memory capacity, leading to the chance behavior observed.