A novel mechanism of dissipation in the form of the traveling waves in twisted nematic liquid crystal cells has been investigated. It has been shown that the traveling waves, tinder influence of an external electric field, directed parallel to both glass plates, are excited in the twisted cells. It is found that the slowest velocity of the traveling front is proportional to the field strength, and, approximately, is three times higher than the front velocity corresponding to the non-traveling Solution. The value of the critical electric field which may excite the traveling waves in the twist cell is pi times less than the value of the threshold electric field for the untwisted geometry.