We report on symmetry properties of tensorial effective transport coefficients characteristic of manytransport phenomena in porous systems at the macroscopic scale. The effective coefficients in themacroscopic models (derived by upscaling (volume averaging) the governing equations at the underlyingscale) are obtained from the solution of closure problems that allow passing the informationfrom the lower to the upper scale. The symmetry properties of the macroscopic coefficients areidentified from a formal analysis of the closure problems and this is illustrated for several differentphysical mechanisms, namely, one-phase flow in homogeneous porous media involving inertialeffects, slip flow in the creeping regime, momentum transport in a fracture relying on the Reynoldsmodel including slip effects, single-phase flow in heterogeneous porous media embedding a porousmatrix and a clear fluid region, two-phase momentum transport in homogeneous porous media, aswell as dispersive heat and mass transport. The results from the analysis of these study cases aresummarized as follows. For inertial single-phase flow, the apparent permeability tensor is irreduciblydecomposed into its symmetric (viscous) and skew-symmetric (inertial) parts; for creeping slip-flow,the apparent permeability tensor is not symmetric; for one-phase slightly compressible gas flow inthe slip regime within a fracture, the effective transmissivity tensor is symmetric, a result that remainsvalid in the absence of slip; for creeping one-phase flow in heterogeneous media, the permeabilitytensor is symmetric; for two-phase flow, we found the dominant permeability tensors to be symmetric,whereas the coupling tensors do not exhibit any special symmetry property; finally for dispersive heattransfer, the thermal conductivity tensors include a symmetric and a skew-symmetric part, the latterbeing a consequence of convective transport only. A similar result is achieved for mass dispersion.Beyond the physical mechanisms under consideration in the present work, the reported technique canbe viewed as a general methodology applicable to any type of upscaled model obtained by volumeaveraging.Read less <