Can connectionist networks effectively represent and process structure? A technique called ‘tensor product representations’, which formalizes and generalizes the approaches of several previous connectionist models, was developed by Smolensky and shown to possess a number of desirable general properties. This paper shows how the technique can be effectively used to design a specific symbol-processing task: the serial execution of simple production rules requiring pattern matching, variable binding and structure manipulation. This ‘Tensor Product Production System’ is applied to one of the classes of production rules in Touretzky and Hinton's Distributed Connectionist Production System, and a number of comparisons are made between the two approaches. The mathematical simplicity and analyzability of the tensor product scheme allows the straightforward design of a simpler, more principled, and in some ways more efficient system.