Chayes L., Shlosman S.B., Zagrebnov V. A. Discontinuity of the Magnetization in Diluted $O(n)$--Models. (554K, Postscript) ABSTRACT. We study the annealed site--diluted versions of the classical $O(n)$ Heisenberg ferromagnets. It is shown that if the temperature is low enough, then at some value of the chemical potential there is phase coexistence between a magnetized, high--density state (liquid-crystal state) and a low density state (gaseous state) with no magnetic order.