NREM sleep is characterized by K-complexes (KCs), over the negative phase of which we identified brief activity in the theta range. We recorded high resolution EEG of whole-night sleep from seven healthy volunteers and visually identified 2nd and 3rd stage NREM spontaneous KCs. We identified three major categories: (1) KCs without intra-KC-activity (iKCa), (2) KCs with non-oscillatory iKCa, and (3) KCs with oscillatory iKCa. The latter group of KCs with intra-KC-oscillation (iKCo), was clustered according to the duration of the iKCo. iKCa was observed in most KCs (1150/1522, 75%). iKCos with 2, 3, and 4 waves were observed in 52% (786/1522) of KCs in respective rates of 49% (386/786), 44%, and 7%. Successive waves of iKCos showed on average a shift of their maximal amplitude in the anterio-posterior axis, while the average amplitude of the slow KC showed no spatial shift in time. The iKCo spatial shift was accompanied by transient increases in instantaneous frequency from the theta band toward the alpha band, followed by decreases to upper theta. The study shows that the KC is most often concurrently accompanied by an independent brief iKCo exhibiting topographical relocation of amplitude maxima with every consecutive peak and transient increases in frequency. The iKCo features are potentially reflecting arousing processes taking place during the KC.