Anxiety has a significant impact on the effectiveness of cognitive activity, which may be due to the peculiarities of the organization of voluntary and involuntary attention in individuals with different anxiety. Aim: to examine functional cortical connections in subjects with different levels of trait anxiety in a state of relative rest and when performing an attention test with usage of the coherent analysis of the teta1-band EEG (4–6 Hz). Coherence of teta1-band of EEG was analyzed in subjects (43 people, men aged 19–21 years) with low, medium and high level of trait anxiety (TA, according to C.D. Spielberger) in three experimental situations: the state of relative rest with closed eyes, the initial state before performing the test (with eyes opened) and during the test (red-black tables of F.D. Gorbov). Subjects with high TA in the state of relative rest with their eyes closed had a lower right-hemisphere coherence of the teta1-band EEG in the system of interrelations with focus in the temporal lead. In the initial state, with eyes opened and during test performing, individuals with high TA showed high level of interhemispheric coherence of the teta1-band of EEG. The highest lability of the structure of coherent relationships in the teta1-range of the EEG was observed in subjects with medium TA, who demonstrated an increase mainly in the interhemispheric coherence of most areas of the cortex during the test compared to the initial state. Individuals with high TA were characterized by relative inertia of the structure of coherent relationships in the teta1-range of the EEG at the stages of examination. The results of the study indicate that trait anxiety is one of the factors modulating the organization of neurocognitive networks both in a state of relative rest and during attention testing.