We assess the impact of being able to substitute an unlimited but costly energy substitute (like wind, solar) for a non-renewable resource (like oil, coal) in a model of sustainable growth. The prospects for sustainability on the optimal path depend crucially on the costs of this substitute.Furthermore, the poorer a country, measured in terms of capital stock at a given point in time, the later it should switch to the renewable substitute, and the more likely it will be unsustainable. Taking learning-by-doing in account, we find that this leads to an earlier switching time but does not guarantee sustainability.JEL Classification: Q21, Q32, Q42, Q56. Key words: backstop technology; non-renewable resource; resource substitution; sustainability; learning-by-doing. * EconomiX, University of Paris Ouest and Climate Economics Chair, e-mail: pjouvet@u-paris10.fr. † Banque centrale du Luxembourg, 2, boulevard Royal, L-2983 Luxembourg, Luxembourg, email: ingmar.schumacher@bcl.lu. We are grateful to Katheline Schubert for discussions and thank two anonymous referees as well as the editor for their comments. The views and opinions expressed here do not necessarily reflect those of the Banque centrale du Luxembourg.