Fluctuation-induced interactions between anisotropic objects immersed in a nematic liquid crystal are shown to depend on the relative orientation of these objects. The resulting long-range "Casimir" torques are explicitely calculated for a simple geometry where elastic effects are absent. Our study generalizes previous discussions restricted to the case of isotropic walls, and leads to new proposals for experimental tests of Casimir forces and torques in nematics.Pacs numbers: 68.60. Bs, 61.30.Hn, 61.30.Dk In the last decade, much theoretical attention has been paid to "Casimir" forces in structured complex fluids [1][2][3]. The pioneering work of Casimir showed that two uncharged conducting plates attract each other in vacuum, due to the modification of the electromagnetic fluctuations imposed by the plates [4]. In complex fluids, similar interactions should exist between embedded objects, as the thermal fluctuations of the medium's elastic distortions are restrained by the boundary conditions imposed by the objects. These interactions are believed to act between bounding surfaces or immersed inclusions in critical fluids or superfluids [5,6], in liquid crystals [7][8][9][10], in bilayer membranes [11][12][13], and also between rodlike polyelectrolytes [14][15][16][17]. Nematic liquid crystals are anisotropic fluids with a quadrupolar longrange order. They are considered as good candidates for the direct observation of "Casimir" interactions in complex fluids. However, clear experimental evidences have to date been scarce [2]. This is probably due to the weakness of fluctuation-induced effects when compared to that of permanent elastic distortions, which are often present.Although nematic liquid crystals are well-known to display orientational effects [18], no "Casimir" interaction directly connected to these orientational properties of nematics have so far been discussed. Here, we demonstrate that thermal fluctuations in nematic liquid crystals can induce torques between bounding surfaces [19]. The existence of "Casimir" torques between objects embedded in complex fluids is usually caused by the anisotropy in the shape of the objects [12,15,17]; here we report on a more subtle effect occurring between infinite plates with translational symmetry. To emphasize the "Casimir" effect, we focus on a situation in which no average elastic distortion is present: two parallel plates with a surface energy favoring an orientation of the local average molecular alignment (director) perpendicular to the surfaces. The ground state is therefore the distorsionless state in which the director is everywhere perpendicular to the boundaries. A "Casimir" torque can arise due to the anisotropy in the rigidity of the surface energy: we assume that deviations from the preferred normal surface orientation is easier in one direction than in the orthogonal one. (This property can be experimentally obtained from a grating surface treated for homeotropic anchoring [20], or by depositing on top of a substrate which is conventionally trea...