We have conducted a series of MEG experiments based on the covert picture-naming task with fourteen non-native English speakers, who made up three groups with different kinds of language training and proficiencies. We found two stages of brain response, corresponding to sensory and semantic processing, which differed in spatio-temporal cortical activation. The active regions found in our two-stage response are consistent with the active regions found in other studies based on techniques such as fMRI, ECoG, and direct electrical stimulation. The sensory processing stage remained uniform across the three differently proficient groups, whereas the semantic processing stage showed inconsistencies. A new understanding of the mechanisms of covertly naming pictures and their neuronal substrate has been obtained. The complete mechanism of the semantic processing stage seems to be much more complex and requires further work. It seems that there are bidirectional connections between the three-focal network formed by fusiform gyrus, Broca's area, and Wernicke's area, and their causal relationships need to be investigated in the future. The connections of this network with the intraparietal sulcus also need to be investigated. In addition, a robust method to identify evoked response peaks needs to be developed in future. Finally, this work highlights the importance of fusiform gyrus, which is at risk of resection in mesial temporal lobe epilepsies.