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We analyze the two-dimensional distribution and kinematics of the stars as well as molecular and ionized gas in the central few hundred parsecs of five active and five matched inactive galaxies. The equivalent widths of the Brγ line indicate that there is no ongoing star formation in their nuclei, although recent (terminated) starbursts are possible in the active galaxies. The stellar velocity fields show no signs of non-circular motions, while the 1-0 S(1) H2 kinematics exhibit significant deviations from simple circular rotation. In the active galaxies the H2 kinematics reveal inflow and outflow superimposed on disk rotation. Steady-state circumnuclear inflow is seen in three active galactic nuclei (AGNs), and hydrodynamical models indicate it can be driven by a large-scale bar. In three of the five AGNs, molecular outflows are spatially resolved. The outflows are oriented such that they intersect, or have an edge close to, the disk, which may be the source of molecular gas in the outflow. The relatively low speeds imply the gas will fall back onto the disk, and with moderate outflow rates, they will have only a local impact on the host galaxy. H2 was detected in two inactive galaxies. These exhibit chaotic circumnuclear dust morphologies and have molecular structures that are counter-rotating with respect to the main gas component, which could lead to gas inflow in the near future. In our sample, all four galaxies with chaotic dust morphology in the circumnuclear region exist in moderately dense groups with 10-15 members where accretion of stripped gas can easily occur. © 2014. The American Astronomical Society. All rights reserved..