A spherical and large-velocity-gradient model is adopted for the theoretica
l calculations of NGC 7027, AFGL 2688 and IRC+10216, whose emissions of CO
far-infrared lines are comparatively strong. The statistical equilibrium ca
lculations cover 107 energy levels. The upper energy limit is 4863 cm(-1) a
bove the energy level with v = 0 and J = 0. There are altogether 107 energy
levels with v = 0, J = 0 - 50; v = 1, J = 0 - 37 and v = 2, J = 0 - 17. Th
e relative flux distributions of the CO lines, as functions of the upper ro
tational quantum number J, of the line, may be a good probe to examine the
physical conditions of the region in which the CO line emissions arise. The
CO far-infrared lines of IRC + 10216 are excited mainly by the central sta
r, while for NGC 7027 and AFGL 2688 by the shocked warm and dense gases. Th
e excitation mechanism is also discussed for other observed objects by usin
g ISO. The CO spectra in the wavelength range 67-186 mu m are important pro
bes for detecting objects with kinetic temperatures of several hundred degr
ees, i.e. the envelopes of carbon- or oxygen-rich stars, planetary nebulae,
young stellar objects and star-forming complexes.