In this paper, I review matching models of dual labor markets from a theoretical point of view and describe the consequences of the most common sets of assumptions on job creation. I assert that two poles arise in the literature depending on the modeling of fixed-term contracts. Some papers assume that fixed-term contracts are flexible in the sense that firm-worker matches may costlessly separate any time. Others assume that a fixed-term match is rigid and cannot split before reaching its stipulated termination date, regardless the undergone shocks. Modeling fixed-term contracts as utterly flexible tends to make fixed-term contracts the only vehicle of job creation, while open-ended contracts only appear as converted expiring fixed-term contracts. This counter-factual result encourages the use of ad hoc hiring rules that ensure that job creation involves both contracts. On the contrary, modeling fixed-term contracts as rigid makes fixed-term contracts less attractive and leaves more room for job creation to involve open-ended contracts. Substitution effects between contracts can be considered in these frameworks. I build up a model with rigid fixed-term contracts and heterogeneous productivity of matches assumption by assumption and find major robustness issues. Introducing the convertibility of fixed-term contracts into open-ended ones flips over the ranking of contracts at the hiring stage with respect to productivity. Enabling matches to optimize the average duration of fixed-term contracts leads to highly counter-factual results: the shortest and the least productive fixed-term matches have the highest probabilities to be converted to open-ended contracts. The highlighted robustness issues and counter-factual predictions contaminate recent papers studying labor market dualism and heterogeneity in workload fluctuations.