This paper deals with research on the development of infants' ability to perceive invariant features of things and the relation of objects to both the spatial layout of the infants' environment and to themselves. Basic assumptions regarding the perception of invariance are discussed and a theoretical view of the role of motion in the development of invariance perception is described. Two types of continuous change from which infants can extract information about invariance are identified: (1) transformations in which the perspective of solid objects changes indicating object rigidity and (2) deformations in which the shape of objects changes, indicating object elasticity. Three experiments are described in which the information extracted by infants from these two types of changes was examined. Subjects in these experiments ranged in age from 3- to 5-months of age and a habituation-dishabituation paradigm was employed. Results of these experiments were interpreted as showing that infants at 3 months are capable of picking up two kinds of invariant properties within an event: (1) information specifying shape of an object while the object is in continuous and even changing motion; and (2) information specifying a type of motion when the objects undergoing motion are different shapes. (JMB)