We investigate the properties of the dispersion tensor in porous media by making use of the method of homogenization by multiple scale expansions, which gives the dispersion model from the pore scale description. Results are valid for random or periodic structures as well. By investigating the domain of relatively small Peclet numbers, we show that the dispersion tensor is asymmetric in some cases. We also demonstrate that in the whole range of validity of the dispersion equation, the dispersion tensor verifies D-ij(dis) (grad x p) = D-ji(dis) (-grad x p). Links with Onsager's relations are given. Numerical investigations at finite Peclet numbers confirm the possible asymmetry of the dispersion tensor.