Although the Surinamese Creoles have figured prominently in discussions about Creole genesis, little is still known about the origin of their TMA system, a central area of grammar that has received much attention in this debate. In this paper we assess the relative contribution of the primary substrate input, varieties of Gbe, to the TMA system. Drawing on both contemporary data from several Surinamese Creoles and varieties of Gbe, and historical data from Sranan Tongo, we show that the substrate was clearly responsible for the emergence of some aspect and tense categories. However, in itself, substrate influence cannot explain the emergence of the entire Creole tense and aspect system. Other processes such as internal change, superstrate influence etc. also played an important role.