Based on CO (2-1) observations obtained with the Swedish-ESO Submillimeter
Telescope, the distribution of molecular material associated with the Wolf-
Rayet ring nebula NGC 2359 has been determined. The angular resolution is 2
2 ", and the velocity resolution is 0.33 km s(-1). Three molecular componen
ts are detected in the direction of the nebula. The bulk of the molecular g
as is observed at 54 km s(-1) and follows the southeastern border of the ne
bula. Adopting a distance d = 5 kpc for NGC 2359, an H-2 mass of about 1200
+/- 500 M. appears to be related to the southern part of the nebula, while
140 +/- 50 M. are linked to the filamentary windblown bubble. The volume d
ensity of the molecular gas related to the southern bar is greater than or
equal to 10(3) H-2 molecules cm(-3), while lower densities were estimated f
or the material associated with the filamentary windblown bubble. From the
present data, it is not clear if the molecular gas at 37 km s(-1) (similar
or equal to 380 +/- 120 M., d = 5 kpc) is associated with the nebula, but t
he molecular material observed at 67 km s(-1) (similar or equal to 70 +/- 2
5 M., d = 5 kpc) seems to be unconnected. The comparison between ionized, H
I, and molecular distributions indicates that the H I filament detected wi
th the Very Large Array is located at the interface between the ionized and
molecular material, and that the H I filament at 54 km s(-1) has originate
d in the photodissociation of the H-2. Most of the molecular gas associated
with the filamentary bubble seems to be interstellar in origin. The dynami
cs of the nebula is reanalyzed based on these new molecular results. It is
consistent with either momentum conservation or an intermediate stage betwe
en energy and momentum conservation.