  The low-lying level schemes and electromagnetic transitions of $^{109}$Te,
$^{109}$I, and the neighboring even-even nucleus $^{108}$Te, are calculated
within the framework of the $SD$-pair approximation of the nuclear shell model.
Good agreement is obtained between the calculated results and experimental
data. The favored components of low-lying bands are discussed in the collective
nucleon-pair subspace. The weak-coupling picture shown in these nuclei and its
relationship with residual quadrupole-quadrupole interaction between valence
protons and neutrons are analyzed.
