In living tissue, membrane-bound organelles, including mitochondria, move along parallel cytoplasmic pathways. Motion is directed and tends to be confined to a single path. Deviations from this single path motion are rare. When present, however, they tend to occur at points of intersection of cytoskeletal linear elements (LE). Such intersections are relatively uncommon in intact axons and extruded axoplasm. However, we have found that such intersections can be produced in extruded preparations by shear forces directed tangential to the axoplasmic surface. We have studied the detailed behavior of mitochondria in extruded squid axoplasm. Special attention was directed to the relationship between mitochondrial shape changes and orientation of cytoskeletal LE. The most striking of these changes in shape is branching. In this process, the mitochondrion transiently assumes a triradial (three-ended) shape. This appearance may be maintained for seconds to minutes before the normal cylindrical shape is resumed by absorption of either the newly formed end or, more commonly, one of the original ends. The frequency of branching appears to be dependent on the degree of cytoskeletal organization. It becomes more common as the number of apparent intersections between cytoskeletal LE increases. Further, the formation of new ends seems to occur along paths defined by cytoskeletal elements. These observations suggest that the mitochondrial membrane is multivalent. That is, it contains multiple sites capable of interacting with the axonal force generation apparatus. Furthermore, LE in the cytoskeleton may indicate the paths along which these interactions are permissible.