Stellar Kinematics of the Spiral Structure in the Solar Neighborhood

We present a method, based on the kinematic analysis of the Galactic disk stars, to clarify whether the internal motions of the stellar system in spiral arms follow those expected in the density wave theory. The method relies on the comparison with the linear relation between the phases of spatial positions and epicyclic motions of stars, as drawn from the theory. The application of the method to the 78 Galactic Cepheids near the Sun, for which accurate proper motions are available from the {\it Hipparcos} Catalogue, has revealed that these Cepheids hold no correlation between both phases, thereby implying that their motions are in contradiction with the theoretical predictions. Possible reasons for this discrepancy are discussed and future prospects are outlined.