Financial stability discussions have mainly revolved around the degree of leverage in financial institutions. Yet, some authors have argued that there might be mechanisms associated with unleveraged institutions that could entail financial instability. We aim to shed light on the possible presence of run-like dynamics in the bond fund flows to and from a group of Emerging Market Economies (EMEs). We examine some of the US monetary policy's implications on these dynamics. As argued, e.g., in Feroli et al. (2014), given the type of incentives many funds face, run-like dynamics might take place, although such funds are mostly unleveraged. We find evidence of the presence of runlike dynamics in the bond flows in several EMEs. We also find evidence that changes in US monetary policy affect such dynamics. Evidently, run-like dynamics could potentially take place in the future.