A related term is positional cycle (repeating the position) in contrast to situational cycle (repeating the situation including the status whose turn it is). See also cycle law.
Herman: This page uses an incorrect definition of cycle, and so the "almost cycle" is in fact just a real cycle according to the commonly accepted definition. As such, I don't see much point in keeping this page.
RobertJasiek: I added the second paragraph but would not mind if the page should be deleted. I am just not sure whether the creator of the term has something extra in mind when referring to odd length. If this aspect is nothing but a desparate attenpt at definition, delete the page.