  We study Poncelet's Theorem in the four non-isomorphic finite projective
planes of order 9. Among these planes, only the Desarguesian plane turns out to
be a Poncelet plane, while the other three planes which are constructed over
the miniquaternion near-field of order 9, are not. This gives a complete
discussion of Poncelet's Theorem in finite projective planes of order 9.
