The center of the edge-on spiral galaxy NGC 891 has been mapped in the J=2-1 and J=1-0 transitions of (CO)-C-12 using the IRAM 30m telescope, with spatial resolutions of 13'' and 21'' respectively. The kinematics of molecular gas in the inner regions of the galaxy is particularly distorted. The position-velocity diagram (p-v) taken along the kinematical major axis of NGC 891 is strikingly similar to the Galaxy's longitude-velocity plot (I-v). As in our Galaxy, we have detected in NGC 891 molecular gas circulating at velocities 'forbidden' by a law based only on circular rotation. Following the work of Binney et al. (1991) on the interpretation of our Galaxy's CO I-v diagram, we have developed a model on the gas kinematics of the inner regions of NGC 891 that explains satisfactorily the major features of the CO p-v diagram. In our model, the flow of molecular gas is driven by a bar that has corotation at r similar to 3 kpc and that is viewed at an angle alpha similar to 45 degrees from its major axis. Molecular clouds circulate along x(2) orbits (elliptical orbits perpendicular to the bar) between the two Inner Linblad Resonances (ILR), and partly populate x(1) orbits (ellipses parallel to the bar) in the outer regions (from the outer ILR up to the corotation circle). We can also explain the radial distribution of molecular gas: the great ring of molecular material at r similar to 4.5-6 kpc might be associated with the Outer Linblad Resonance of the bar (OLR) and the adjacent hole of molecular gas inside this radius, with the corotation circle. The observed kinematics of molecular gas in the center of the edge-on spiral NGC 5907, as well as a number of other galaxies, could be also interpreted in terms of highly elliptical orbits driven by bars or triaxial potentials.