I will propose a tentative framework of how words in two languages could be organized in the cerebral cortex based on neural assembly theory, according to which neurons that fire synchronously are bound into large-scale distributed functional units (assemblies), which represent a mental event as a whole ("gestalt"). For language this means a word is engendered by widely distributed cell assemblies in which the different linguistic constituents are grouped together in action-perception circuits and become activated in parallel. In this article I will discuss the advantages of assembly coding over the traditional hierarchical convergence scheme. Recent evidence from language comprehension and production supporting the notion of neural assemblies representing words are discussed and a spatiotemporal model for word production based on this concept is presented. Finally, I will show how this view may be generalized to bilingualism and explain mechanistically some key phenomena in the literature.