  The structure of the commutative Moufang loops (CML) with minimum condition
for subloops is examined. In particular it is proved that such a CML $Q$ is a
finite extension of a direct product of a finite number of the quasicyclic
groups, lying in the centre of the CML $Q$. It is shown that the minimum
conditions for subloops and for normal subloops are equivalent in a CML.
Moreover, such CML also characterized by different conditions of finiteness of
its multiplication groups.
