Functional devices and circuits based on Resonant Tunnelling Diodes (RTDs) are receiving much attention since they allow high speed and/or low power operation. RTDs exhibit a negative differential resistance in their current-voltage characteristic which can be exploited to significantly increase the functionality implemented by a single gate in comparison to other technologies. In particular, they have proven to efficiently implement threshold gates which are a generalization of conventional boolean gates. Suitable logic synthesis tools are required to handle these complex building blocks in order to translate the advantages of this emergent technology to the circuit and system levels. This paper describes an efficient approach to the automatic design of networks of threshold gates from functional specifications. Results for widely used logic functions and standard benchmark circuits are reported.