Strong signal of fluctuation superconductivity has been found in RBa2Cu3O7-δ(R = Y, Gd) superconducting thin films near Tc through careful investigation on resistance transitions. Detailed analyses show that, for both polycrystalline and epitaxial YBa2Cu3O7-δ thin films, it tends to be of 2D characteristic when T》Tc, but a crossover from 2D to 3D will occur when T approaches Tc, which is consistent with the prediction of Lawrence-Doniach theory. The 3D-2D crossover can also take place when a rather weak field (1.5G) is applied parallel to Cu-O planes, but it is not the case when H is perpendicular to Cu-O planes, this indicates that there is a weak coupling between Cu-O planes in YBa2Cu3O7-δ. The same study on a GdBa2Cu3O7-δ epitaxial thin films shows that the 2D feature also appeares when T》Tc, but no evidence of 3D has been found when T approaches Tc, this we think is related to the self-moment of Gd ions.