How the cilium appeared is still such a poorly defined question that c
urrent hypotheses range from a symbiotic spirochaete to a cellular eye
. In this paper, the whole question is subdivided into a list of probl
ems which are morphological, physiological and temporal. These problem
s are examined one by one, in order to analyse the most popular exogen
ous hypothesis of Margulis as well as other recent exogenous and endog
enous hypotheses. To overcome fundamental topological and temporal dif
ficulties, a new endogenous hypothesis is expounded, according to whic
h the cilium derives from a cellular peduncle reinforced with microtub
ules. This hypothesis implies a geometrical rationale for the ninefold
symmetry. In the last paragraph the consequences of the various hypot
heses are compared.