In this paper we introduce Semantic Web Spaces, a middleware for coordinating knowledge processes on the Semantic Web. Co-ordination is an important aspect of any type of interaction between computer agents, but we find especially so on the Semantic Web in which the communication contains knowledge rather than data and correct inferences can only be made when the right knowledge is available at the right time. Because of this we have identified tuplespace computing as a relevant paradigm for agent communication on the Semantic Web and have prototypically realized a system based on a Linda-inspired coordination model and on core semantic technologies such as RDF, ontologies and reasoning.