We develope a kinematic model based on a dynamical model of stellar population synthesis. We compare the model predictions with two proper motion catalogues.
The model for deducing the local value of galactocentric gradient of the velociy dispersion is based on the local distribution of the orbital eccentricity e, the mean orbital radius ω and the velocity perpendicular to the galactic plane. We apply it to samples of the Gliese´s catalogue delimited by stars of F,. Gand K spectral types. We obtain for the galactic radial gradient of velocity disperion: -0,2 kpc-1, a value compatible with the Toomre´s local stability criterion.