We describe the general occurrence in animal cells of elastic components (“tethers”) that connect individual chromosomes moving to opposite poles during anaphase. Tethers, originally described in crane-fly spermatocytes, exert force on chromosome arms opposite to the direction the anaphase chromosomes move. We show that they exist in a broad range of animal cells. Thus tethers are previously unrecognised components of general mitotic mechanisms that exert force on chromosomes and they need to be accounted for in general models of mitosis in terms of forces on chromosomes and in terms of what their roles might be.