We study the gas kinematics and chemical abundances in the inner regio
ns of six galaxies with active galactic nuclei. The galaxies were sele
cted for having star-forming regions in rings or spirals within a few
kiloparsecs of the nucleus. The goal of the project is to search for a
ny connections between the gasdynamics, the chemical abundances, and t
he nuclear activity. Narrowband images have been obtained to map out t
he ionized gas. Medium-dispersion long-slit spectroscopy at several po
sitions over the nuclear region has been used to obtain the gaseous ve
locity field and distribution of excitation. The H II regions in the r
ings are located near the turnover point of the rotation curves, sugge
sting association with the inner Lindblad resonance. The nuclear ring
in the LINER NGC 1326 may be located between the two inner Lindblad re
sonances, and the inner rings in the Seyfert 2 galaxy NGC 3081 and the
LINER/Seyfert 1 NGC 7213 may be associated with the Omega - kappa/4 r
esonance. A warm ionized medium (WIM) is found to pervade the inner re
gion in all galaxies. There is a correlation between the [N II]/H alph
a and [S II]/Her ratios and the FWHM of the [N N] lambda 6584 emission
line in this WIM, indicating that shocks contribute to the ionization
of the gas. We show that contamination by this diffuse emission incre
ases the measured [N II]/H alpha and [S II]/H alpha ratios at H II reg
ions close to the nuclei and thus may account, in part, for the system
atically higher [N II]/H alpha and [S II]H alpha found in the present
work and by previous authors for near-nuclear H n regions compared wit
h H n regions farther out in the disk of the galaxy. In the present pa
per, we correct for this contamination by interpolating the contributi
on of the WIM at the H n regions and subtracting it off. Oxygen and ni
trogen abundances are obtained for 18 H II regions and are extrapolate
d to obtain the abundance of the nuclear gas, which is found to range
from solar to 2 times solar for oxygen and from 2 to 4 times solar for
nitrogen. Such values are similar to those observed in nonactive gala
xies with the same luminosity and morphological type and do not suppor
t the idea that the central regions of active galaxies have undergone
unusual chemical processing.