Microtubules (tubulin) or bundles of microfilaments (actin) are thought to cause movement, in some instances, by disassembly or assembly of subunits. Possible examples are the pulling of a chromosome toward a pole in mitosis (anaphase) or the deformation of a cell membrane to change the shape of a cell. This paper examines the relevant elementary bioenergetic considerations when assembly or disassembly of an aggregate occurs against a resisting force. The problem is considered, in the first section, without NTPase activity. Sickle cell hemoglobin aggregation in vivo is an example. In the second section, the tubulin GTPase and actin ATPase activities are included in the analysis.