As a result of the rapid growth of microeconometric studies of exporting firms, we know quite a lot about the hysteresis occurring in the current decision of firms to export. Firms entering a foreign market the previous year are more likely to export the current year. This fact is traditionally interpreted as a consequence of sunk export costs at entry to the international market. These costs are for instance the knowledge of foreign markets, the search for new distribution networks, or the compliance with border crossing standards specific to a given market. The specificity of the destination market appears as being of huge importance for the firms. Papers in this field propose to test for the existence of sunk-cost hysteresis by analysing entry and exit patterns in plant-level panel data, whatever the destination market. Roberts and Tybout (1997) or Özler et al. (2009) develop and estimate a dynamic discrete-choice model of the plant’s current exporting status in Colombia or Turkey respectively. Only a few studies have accounted either for the destination of the exports or for the volume exported. Blanes-Cristobal et al. (2008) show that previous experience on a market has a positive impact on the probability of current export on this market. Das et al. (2007) consider both the decision to export and the value exported in a dynamic model. They show that entry costs on international markets (whatever the destination market) are substantial. The questions addressed by this study are: Are sunk costs a feature of the firm's export behavior (decision and volume) and do they vary across export markets? A multivariate dynamic panel model of French agribusiness firms' exports to two aggregate markets (EU and Rest of the World) is specified. The model accounts for both zero level and positively skewed exports by adopting the Cragg (1971) logarithmic Tobit model. Unobserved firm-level heterogeneity is accounted for by introducing random effects which may be correlated across export markets. The initial conditions problem is treated by assuming that a component of the unobserved firm effect is conditional on initial values and exogenous variables (Wooldridge, 2005). As a consequence the degree of structural state dependence can be estimated for each export market. Previous export experience in both markets is hypothesized to impact both the decision to export and the level of exports in each market.