  Within the NUclei of GAlaxies project we have obtained IRAM PdBI and 30m
12CO(1-0) and 12CO(2-1) observations of the spiral galaxy NGC 6951. Previous
work shows that there is indirect evidence of gas inflow from 3 kpc down to
small radii: a large-scale stellar bar, a prominent starburst ring (r~580 pc)
and a LINER/Seyfert 2 nucleus. In this paper we study the gas kinematics as
traced by the CO line emission in detail. We quantify the influence of the
large-scale stellar bar by constructing an analytical model of the evolution of
gas particles in a barred potential. From this model gravitational torques and
mass accumulation rates are computed. We compare our model-based gravitational
torque results with previous observationally-based ones. The model also shows
that the large-scale stellar bar is indeed the dominant force for driving the
gas inward, to the starburst ring. Inside the ring itself a nuclear stellar
oval might play an important role. Detailed analysis of the CO gas kinematics
there shows that emission arises from two co-spatial, but kinematically
distinct components at several locations. The main emission component can
always be related to the overall bar-driven gas kinematics. The second
component exhibits velocities that are larger than expected for gas on stable
orbits, has a molecular gas mass of 1.8x10^6Msun, is very likely connected to
the nuclear stellar oval, and is consistent with inflowing motion towards the
very center. This may form the last link in the chain of gas inflow towards the
active galactic nucleus in NGC 6951.
