Context :

Aims : We determine carbon , oxygen , and their isotopic abundances based on CO and OH spectra in 23 red giant stars , and identify possible origin of difficulty in abundance analysis of cool luminous stars .

Methods : We apply the line-by-line analysis based on the classical micro-turbulent model and 1 D model photospheres .

Results : We found purely empirically that there is a critical value of log { W / \nu } \approx - 4.75 ( W is the equivalent width and \nu the wavenumber ) above which the observed lines do not follow the classical line formation theory based on the micro-turbulent model and that the classical abundance analysis can be applied only to the weak lines of log { W / \nu } \la - 4.75 .
The carbon , oxygen , and their isotopic abundances in 23 K - M giant stars obtained from such weak lines are roughly consistent with the recent evolutionary models , although the ^ { 12 } C/ ^ { 13 } C puzzle remains unsolved .
On the other hand , it is already known that the very strong lines of log { W / \nu } > -4.4 are contaminated by the contribution from extra molecular layers .
The less strong but saturated lines of -4.75 < { log } { W / \nu } \la - 4.4 ( intermediate-strength lines ) can not be understood at all with the abundance and turbulent velocity based on the weak lines .
From the behavior shown by these lines and considering other observations such as the detection of H _ { 2 } O lines , not only in the late M giants but also in the early M and K giants , we found that the intermediate-strength lines are essentially the same as the strong lines in that they also include contamination from the extra molecular layers .
Thus the behavior of the intermediate-strength lines , including those with LEP as high as 2 eV , appears to be nothing but a manifestation of the warm molecular envelope or MOLsphere .

Conclusions : The infrared spectra of K - M giant stars are a hybrid of at least two components originating in the photosphere and MOLsphere .
Only the weak lines , mostly high excitation , are relatively free from the effect of MOLsphere and can be used to extract photospheric abundances .
The strong lines and the intermediate-strength lines which actually dominate the observed infrared spectra , are badly disturbed by contamination from the MOLsphere .
For this reason , they provide little information about the photosphere , but instead can be new proves of the warm molecular envelope for which little is known yet .
In the interpretation and analysis of the infrared spectra of K - M giant stars , it is essential to keep their hybrid nature in mind .