Until recently, the correlation between the IRAS flux density at 60 mu
m, S-60, and the intensity of the CO(1-0) line seemed well establishe
d for O-rich evolved stars with intermediate mass-loss rates (similar
to 10(-6) to 10(-5) M./yr). This observational correlation was in agre
ement with theory of mass-loss rates. On the basis of more sensitive C
O(1-0) observations performed with the IRAM-30m antenna, we show that
a large group of infrared sources do not follow this correlation. Almo
st 50% of the infrared O-rich sources in our sample (IRAS flux ratio S
-25/S-12 from 0.69 to 1.20) have ''weak'' CO emission relative to S-60
. These sources are more concentrated towards the Galactic plane. The
majority of them have early spectral types and low IRAS variability in
dex, and are thus probably supergiants, as it is already established f
or many of them and can be understood from theoretical considerations,
mainly related to the large luminosity of the supergiants. We conclud
e that all those with ''normal'' CO emission (i.e. a low S-60/T-mb(1-0
) ratio) are AGB stars. Possible origins of the ''weak'' CO emission o
bserved in a few AGB stars are briefly discussed.