For an optimal control problem with an infinite time horizon, assuming various terminal state conditions (or none), terminal conditions for the costate are obtained when the state and costate tend to limits with a suitable convergence rate. Under similar hypotheses, the sensitivity of the optimum to small perturbations is analysed, and in particular the stability of the optimum when the infinite horizon is truncated to a large finite horizon. An infinite horizon version of Pontryagin's

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... is also obtained. The results apply to various economic models.