  We study the Casimir-Polder potential of a multilevel alkali-metal atom near
an optical nanofiber. We calculate the mean potential of the atom in a
fine-structure level. We perform numerical calculations for the Casimir-Polder
potentials of the ground state and a few low-lying excited states of a rubidium
atom. We show that, unlike the potential of the ground state, which is negative
and attractive, the potential of a low-lying excited state may take positive
values, oscillate around the zero value with a decaying amplitude, and become
repulsive in some regions of atom-to-surface distances. We observe that, for a
nanofiber with a radius of 200 nm, the potential for the state $8S_{1/2}$ of a
rubidium atom achieves a positive peak value of about 17 $\mu$K at a distance
of about 150 nm from the fiber surface, and becomes rather strongly repulsive
in the region of distances from 150 to 400 nm. We also calculate the
nanofiber-induced shifts of the transition frequencies of the atomic rubidium
$D_2$ and $D_1$ lines. We find that the shifts are negative in the region of
short distances, become positive, and oscillate around the zero value with a
decaying amplitude in the region of large distances.
