Weakly stationary fields of random quasiellipsoids (rigid or flat ellipsoids) in Rnare intersected with a fixed hyperplane H. The stereological problem consists in determining the size and shape distribution of a “typoical” quasiellipsoid of the sample by selectional data. The size is assumed to be independent of shape and directins. In general the problem cannot be solved uniquely (s.[1]). In the present paper the question is answered for which shape–direction distributions the stereological formulas for all size distributions are the same as in the well–known spherical case