  We study the effective interaction between two ellipsoidal particles at the
interface of two fluid phases which are mediated by thermal fluctuations of the
interface. In this system the restriction of the long--ranged interface
fluctuations by particles gives rise to fluctuation--induced forces which are
equivalent to interactions of Casimir type and which are anisotropic in the
interface plane. Since the position and the orientation of the colloids with
respect to the interface normal may also fluctuate, this system is an example
for the Casimir effect with fluctuating boundary conditions. In the approach
taken here, the Casimir interaction is rewritten as the interaction between
fluctuating multipole moments of an auxiliary charge density--like field
defined on the area enclosed by the contact lines. These fluctuations are
coupled to fluctuations of multipole moments of the contact line position (due
to the possible position and orientational fluctuations of the colloids). We
obtain explicit expressions for the behavior of the Casimir interaction at
large distances for arbitrary ellipsoid aspect ratios. If colloid fluctuations
are suppressed, the Casimir interaction at large distances is isotropic,
attractive and long ranged (double--logarithmic in the distance). If, however,
colloid fluctuations are included, the Casimir interaction at large distances
changes to a power law in the inverse distance and becomes anisotropic. The
leading power is 4 if only vertical fluctuations of the colloid center are
allowed, and it becomes 8 if also orientational fluctuations are included.
