The stability of the elliptical orbits of diamagnetic positronium is s
tudied and it is found to depend only on the eccentricity epsilon and
the combination of parameters lambda=B(2)r(0c)(3) (where B is the magn
etic field strength and r(0c) the conserved guiding center). For small
and large values of lambda the orbits remain stable while at approxim
ately lambda=1 unstable behavior appears when the eccentricity becomes
larger than epsilon=0.25. (C) 1997 Elsevier Science B.V.