  We identified a possible origin of the difficulty in abundance analysis of
cool luminous stars. We found purely empirically that there is a limit of
logW/nu = -4.75 (W: equivalent width, nu: wavenumber) above which the observed
lines do not follow the line formation theory based on the classical
micro-turbulent model and that the abundance analysis can be done only with the
lines of logW/nu < -4.75. The C, O, and their isotopic abundances determined
from such weak lines of CO and OH in 23 K - M giants are roughly consistent
with the predictions of evolutionary models. However, the stronger lines of
logW/nu > -4.75 cannot be analyzed at all by the classical line formation
theory. From the behavior of these lines and considering other observations
such as the detections of H2O lines, not only in the late M giants but also in
the early M and K giants, we found that these lines are badly disturbed by the
contamination from extra molecular layers. We already know that the very strong
lines of logW/nu > -4.4 are contaminated by the contribution from the extra
warm molecular layers, but we now show that such contamination should be
prevailing not only in the strong low excitation lines but also in the
intermediate-strength lines (-4.75 < logW/nu > -4.4) as well. The reason why
these lines cannot be used for determining photospheric abundances is simply
because they include the contamination of the non-photospheric origin. Instead
they can be new proves of the warm molecular envelope for which little is known
yet. An important conclusion is that the infrared spectra of K - M giants are a
hybrid of at least two components originating in the photosphere and the warm
molecular envelope. In the interpretation and analysis of the infrared spectra
of cool luminous stars, it is essential to keep their hybrid naure in mind.
