We study the kinematics of a local sample of stars, located within a cylinder of 500 pc radius centered on the Sun, in the RAVE data set. We find clear asymmetries in the vR v∞ velocity distributions of thin and thick disk stars: there are more stars moving radially outward for low azimuthal velocities and more radially inward for high azimuthal velocities. Such asymmetries have been previously reported for the thin disk as being due to the Galactic bar, but this is the first time that the same type of structures are seen in the thick disk. Our findings imply that the velocities of thick-disk stars should no longer be described by Schwarzschilds, multivariate Gaussian or purely axisymmetric distributions. Furthermore, the nature of previously reported substructures in the thick disk needs to be revisited as these could be associated with dynamical resonances rather than to accretion events. It is clear that dynamical models of the Galaxy must fit the 3D velocity distributions of the disks, rather than the projected 1D, if we are to understand the Galaxy fully.