  This paper studies the global ISM content in a sample of 104 accreting
galaxies, including counterrotators and polar rings, which spans the entire
Hubble sequence. The molecular, atomic and hot gas content of accretors is
compared to a newly compiled sample of normal galaxies. We present results of a
small survey of the J=1--0 line of {12}CO with the 15m SEST telescope on a
sample of 11 accretors (10 counterrotators and 1 polar ring). The SEST sample
is enlarged with published data from 48 galaxies, for which observational
evidence of counterrotation in the gas and/or the stars has been found.
Furthermore, the available data on a sample of 46 polar ring galaxies has been
compiled. It was found that the normalized content of cold gas (M_gas/L_B) in
polar rings is ~1 order of magnitude higher than the reference value derived
for normal galaxies. The inferred gas masses are sufficient to stabilize polar
rings through self-gravity. In contrast, it was found that the cold gas content
of counterrotators is close to normal for all galaxy types. Although
counterrotators and polar rings probably share a common origin, the gas masses
estimated here confirm that light gas rings accreted by future counterrotators
may have evolved faster than the self-gravitating structures of polar rings. In
this scenario, the transformation of atomic into molecular gas could be
enhanced near the transition region between the prograde and the retrograde
disks, especially in late-type accretors characterized by a high content of
primordial gas. This is tentatively confirmed in this work: the measured H_2/HI
ratio seems larger in counterrotators than in normal or polar ring galaxies for
types later than S0s.
