We have defected seven different molecular lines in absorption towards
the remote radio source 1504+377. The absorption occurs in an edge-on
galaxy al a redshift z = 0.672. The absorption splits into several co
mponents, gathered in two groups separated by 330 km s(-1). The two gr
oups are interpreted as coming from a spiral arm and a nuclear ring in
noncircular motion. Given the spatial coincidence of the remote radio
source, and the galaxy as well as the absence of gravitationally lens
ed images, the absorption is likely to originate in the galaxy hosting
the AGN. Comparing different Lines, we fmd a large density for the ab
sorbing molecular clouds, and an excitation temperature of 10-20 K. Th
e HCO+ abundance is enhanced by at least one order of magnitude with r
espect to current chemical equilibrium models. The HNC/HCN ratio yield
s a kinetic temperature in accordance with the excitation temperature.
This suggests a dense medium, however with a low column density, sinc
e the absorption lines are optically thin. A molecular cloud composed
of small dense clumps with a low filling factor could account for that
. We also present a list of upper limits for additional candidates sea
rched for molecular absorption. With previously published negative res
ults, the total number of objects searched is about 50, while 4 absorp
tion systems have been found. We discuss the efficiency of various sel
ection criteria.