Turbellaria Flatworm The Turbellaria flatworm is part of the class Turbellaria. Like other flatworms of this class they are compressed, with high surface area to volume ratios. These flatworms tend to move by coordinated waves of cilia on a secreted mucus trail even though some of these species can swim by rhythmic muscle contractions. Their complexity of their nervous system varies from a simple nerve that are based on pairs of longitudinal nerve cords to an interlacing web of nerves capable of fine muscular control.