  The spiral galaxy NGC 6503 exhibits a regular kinematical structure except
for a remarkable drop of the stellar velocity dispersion values in the central
region. To investigate the dynamics of the disc a theoretical framework has
been described. This includes a mass decomposition of the galaxy into a family
of disc/halo realizations compatible with the observed photometry and rotation
curve. For this family stellar velocity dispersion values and stability
parameters were calculated, showing that the more massive discs, although
having larger dispersions, are less stable. However, a reliable theoretical
description of the inner regions where the drop occurs cannot be given.
  That is why we have resorted to numerical calculations. Pure stellar 3d
simulations have been performed for the family of decompositions. A clear
result is that disc/dark halo mass ratios approaching those of the maximum disc
limit generate a large bar structure. This is incompatible with the observed
morphology of NGC 6503. For the larger radii the stellar kinematics resulting
from the simulations essentially agrees with that predicted by the theory, but
the central velocity dispersion drop could not be reproduced.
  A close inspection reveals that the central nuclear region is very small and
bright. Therefore, tentatively, this nucleus was considered as an isothermal
sphere and a core fitting procedure was applied. For an adopted equal
mass-to-light ratio of disc and nucleus, a velocity dispersion of 21.5 km/s is
predicted, in excellent agreement with the observed central value. The observed
dispersion drop can thus be explained by a separate kinematically distinct
galactic component.
