The remanufacturing process consists in recovering returned products by replacing or repairing components. In this work, we consider an uncapacitated lot-sizing problem with remanufacturing and two types of markets. The demand of new products is only satisfied by manufactured products, whereas the demand of second-hand products is only satisfied by the remanufacturing of returned products. We develop polynomial dynamic programming algorithms for two cases, where the returned products can be disposed or not.