The functional state of subjects with high and low levels of anxiety is studied by electroencephalograph analysis of different temporal periods preceding a cognitive task of visual expression recognition. Several conditions are investigated: background/eyes closed; background/eyes opened; listening to instructions for the cognitive task; operative rest (time lapse between listening to instructions and the beginning of the task); as well as short intervals immediately preceding exposure to target stimuli (preparatory stage), which were paired facial images with identical or different emotional expressions. At all these pre-task stages, high-anxiety subjects exhibit much lower electroencephalograph amplitude values for alpha and theta bands (as compared with low-anxiety subjects). The most prominent differences in electroencephalograph amplitude values revealed during the phases of listening to instructions and operative rest. These datum may provide more precise electrophysiological markers of the level of anxiety during conditions preceding cognitive task performance.