We report $^{12}$CO($J=$3--2) observations of 15 nearby elliptical galaxies carried out with the ASTE telescope. Thirteen were selected without regard to the presence of other tracers of cold interstellar matter. CO emission was detected from three of the galaxies, two of which are undetected by IRAS at 100 microns, suggesting that cold ISM may be present in more ellipticals than previously thought. The molecular gas masses range from $2.2 times 10^6$ to $4.3 times 10^8$ $M_odot$. The ratio of the CO(3--2) and (1--0) lines, $R_{31}$, has a lower value for elliptical galaxies than for spiral galaxies except for NGC 855, for which the value is close to the mean for spirals. The molecular gas in NGC 855 has a mean density in the range 300 -- 1000 cm$^{-3}$ adopting a temperature range of 15 -- 100 K.
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