Most flagellate protozoans possess either one or two flagella extending from the anterior (front) end of the body. Some protozoans, however, have several flagella that may be scattered over the entire body; in such cases, the flagella usually are fused into distinctly separate clusters. Flagellar movement, or locomotion, occurs as either planar waves, oarlike beating, or three-dimensional waves. All three of these forms of flagellar locomotion consist of contraction waves that pass either from the base to the tip of the flagellum or in the reverse direction to produce forward or backward movement. The planar waves, which occur along a single plane and are similar to a sinusoid (S-shaped) wave form, tend to be asymmetrical; there is a gradual increase in amplitude (peak of the wave) as the wave passes to the tip of the flagellum. In planar locomotion the motion of the flagella is equivalent to that of the body of an eel as it swims. Although symmetrical planar waves have been observed, they apparently are abnormal, because the locomotion they produce is erratic. Planar waves cause the protozoan to rotate on its longitudinal axis, the path of movement tends to be helical (a spiral), and the direction of movement is opposite the propagation direction of the wave.

In oarlike flagellar movements, which are also planar, the waves tend to be highly asymmetrical, of greater side to side swing, and the protozoan usually rotates and moves with the flagellum at the forward end. In the three-dimensional wave form of flagellar movement, the motion of the flagella is similar to that of an airplane propeller; i.e., the flagella lash from side to side. The flagellum rotates in a conical configuration, the apex (tip) of which centres on the point at which the flagellum is attached to the body. Simultaneous with the conical rotation, asymmetrical sinusoidal waves pass from the base to the end of the flagellum. As a result of the flagellar rotation and its changing angle of contact, water is forced backward over the protozoan, which also tends to rotate, and the organism moves forward in the direction of the flagellum.

Ciliary locomotion

Cilia operate like flexible oars; they have a unilateral (one-sided) beat lying in a single plane. As a cilium moves backward, it is relatively rigid; upon recovery, however, the cilium becomes flexible, and its tip appears to be dragged forward along the body. Because the cilia either completely cover, as in ciliate protozoans, or are arranged in bands or clumps, the movement of each cilium must be closely coordinated with the movements of all other cilia. This coordination is achieved by metachronal rhythm, in which a wave of simultaneously beating groups of cilia moves from the anterior to the posterior end of the organism. In addition to avoiding interference between adjacent cilia, the metachronal wave also produces continuous forward locomotion because there are always groups of cilia beating backward. Moreover, because the plane of the ciliary beat is diagonal to the longitudinal axis of the body, ciliate organisms rotate during locomotion.

Pseudopodial locomotion

Although ciliar and flagellar locomotion are clearly forms of appendicular locomotion, pseudopodial locomotion () can be classed as either axial or appendicular, depending upon the definition of the pseudopodium. Outwardly, pseudopodial locomotion appears to be the extension of a part of the body that anchors itself and then pulls the remainder of the body forward. Internally, however, the movement is quite different. The amoeba, a protozoan, may be taken as an example. Its cytoplasm (the living substance surrounding the nucleus) is divided into two parts: a peripheral layer, or ectoplasm, of gel (a semisolid, jellylike substance) enclosing an inner mass, or endoplasm, of sol (a fluid containing suspended particles; i.e., a colloid). As a pseudopodium, part of the ectoplasmic gel is converted to sol, whereupon endoplasm begins flowing toward this area, the cell wall expands, and the pseudopodium is extended forward. When the endoplasm, which continues to flow into the pseudopodium, reaches the tip, it extends laterally and is transformed to a gel. Basically, the movement is one of extending an appendage and then emptying the body into the appendage, thereby converting the latter into the former. Although the flow of the cytoplasm is produced by the same proteins involved in the mechanism of muscle contraction, the actual molecular basis of the mechanism is not yet known. Even the mechanics of pseudopodial formation are not completely understood.

Undulating and gliding locomotion

Two other types of locomotion are observed occasionally in protozoans. Some protozoans, usually flagellates, have along their bodies a longitudinal membrane that undulates, thereby producing a slow forward locomotion. A gliding locomotion is commonly seen in some sporozoans (parasitic protozoans), in which the organism glides forward with no change in form and no apparent contractions of the body. Initially, the movement was thought to be produced by ejecting mucus, a slimy secretion; small contractile fibrils have been found that produce minute contraction waves that move the animal forward.