  We study the late time behavior of the slow-roll parameter in the stringy
quintessence model when axion as well as saxion is allowed to move. Even though
the potential is independent of the axion at tree level, the axion can move
through its coupling to the saxion and the background geometry. Then the
contributions of the axion kinetic energy to the slow-roll parameter and the
vacuum energy density are not negligible when the slow-roll approximation does
not hold. As the dimension of the field space is doubled, the fixed point at
which the time variation of the slow-roll parameter vanishes is not always
stable. We find that the fixed point in the saxion-axion system is at most
partially stable, in particular when the volume modulus and the axio-dilaton,
the essential ingredients of the string compactification, are taken into
account. It seems that as we consider more saxion-axion pairs, the stability of
the fixed point becomes difficult to achieve.
