The presence of foreign banks in emerging markets has increased markedly over the last two decades, raising questions about their potentially stabilizing or destabilizing role during times of financial distress. Most studies on this subject have focused on banks' asset side (i.e., their lending behavior). This paper focuses on their liability side, studying the behavior of depositors vis-à-vis foreign banks. We rely on data from the banking crises in Argentina and Uruguay over the period 1994-2002 to conduct the study. The paper focuses on three questions; (i) are foreign banks perceived as a safe haven during bank runs?; (ii) does their legal structure (branch versus subsidiary) matter?; (iii) do perceptions depend on the nature of the crisis? Contrary to the commonly held view that foreign banks play a stabilizing role during domestic banking crises, we do not find robust evidence in this regard. Only in one (large) bank run episode, out of five studied, there is evidence of safe haven perceptions towards foreign branches.