The management of an invasive species presents some similarities with renewable resources. However, the objective function is the sum of two positive and often increasing components : environmental damages and management costs. The paper stresses the importance of stock externalities to ensure that a non zero stock is optimal. In a static approach, the paper shows that when the damage function is always increasing, the absence of stock externalities leads to a solution of eradication (zero stock) under usual assumptions. If the damage is decreasing (and negative as sometimes assumed) it is still possible that a non zero stock to be optimal. In the presence of externalities it is more likely that an interior solution be optimal, although it needs not to be the case. If the cost externalities tend to be infinitely large for low stock levels, then an eradication is ruled out. In the dynamic approach, conditions are given for an interior solution to exist. Again it is shown that the existence of externalities helps satisfy both first and second order (convexity) conditions for a solution stopping short from full eradication. An empirical illustration for Ludwigia spp. will be given at the conference.