  We present 12CO(J=2->1) and CO(J=3->2) observations of quiescent Virgo
Cluster spiral galaxies with the KOSMA 3m submm telescope. The beam sizes of
80" at 345 GHz and 120" at 230 GHz are well suited for the investigation of
global properties of Virgo Cluster galaxies. The observed sample was selected
based on previous 12CO(J=1->0) detections by Stark et al. (1986), performed
with the AT&T Bell Laboratory 7m telescope (beam size 100"). We were able to
detect 18 spiral galaxies in 12CO(2->1) and 16 in 12CO(3->2). Beam matched
observations of the lowest three 12CO transitions allow us to compare our
results with previous high spatial resolution studies of (moderate) starburst
galaxies and galactic core regions. We discuss the global excitation conditions
of the ISM in these quiescent spiral galaxies. The resulting CO (3--2)/(1--0)
integrated line ratios vary over a relatively narrow range of values from 0.35
to 0.14 (on a K km/s-scale) with increasing CO (2--1)/(1--0) ratio (from 0.5 to
1.1). The line ratios between the three lowest rotational transitions of CO
cannot be fitted by any radiative transfer model with a single source
component. A two-component model, assuming a warm, dense nuclear and a cold,
less dense disc component allows us to fit the observed line ratios for most of
the galaxies individually by selecting suitable parameters. The two-component
model, however, fails to explain the observed correlation of the line ratios.
This is due to a variation of the relative filling factor of the warm gas
alone, assuming a typical set of parameters for the two components common for
all galaxies.
