We construct a model of offshoring with externalities and firm heterogeneity. Due to the presence of externalities, temporary shocks like the Y2K problem can have permanent effects, i.e., they can permanently raise the extent of offshoring in an industry. Also, the initial advantage of a country as a potential host for outsourcing activities can create a lock in effect, whereby late movers have a comparative disadvantage. Furthermore, the existence of firm heterogeneity along with externalities can help explain the dynamic process of offshoring, where the most productive firms offshore first and the others follow later. Finally, we show the possibility of complementarity between two modes of offshoring: FDI and offshore outsourcing.