We implement the stable correspondence of a job matching market in Subgame Perfect Equilibrium. We use a simple sequential mechanism in which firms propose a salary to each worker (first stage) and, then, each worker accepts at most one proposal (second stage). Moreover, if agents' preferences are additive, this mechanism implements in Subgame Perfect Equilibrium the firms' optimal corre- spondence when firms use undominated strategies. Finally, we construct another simple sequential mechanism where the order of decisions is permuted and which implements the workers' optimal correspondence when agents' preferences are additive.Journal of Economic LiteratureClassification Numbers: C78, D78. © 1998 Academic Press.