Nanocomposites of three different polyesters with dodecyltriphenylphosphonium-montmorillonite (C12PPh-MMT) as an organoclay are compared with their thermal properties, mechanical properties, and morphologies. Poly(butylene terephthalate) (PBT), poly(ethylene terephthalate) (PET), and poly(trimethylene terephthalate) (PTT) were used as matrix polymers in the fabrication of polyester nanocomposite fibers. The variations of their properties with organoclay content in the polymer matrix and draw ratio (DR) are discussed. Transmission electron microscopy (TEM) micrographs show that some of the clay layers are dispersed homogeneously within the polymer matrix on the nano-scale, although some clay particles are agglomerated. We also found that the addition of only a small amount of organoclay is enough to improve the thermal stabilities and mechanical properties of the polyester nanocomposite fibers. Even polymers with low organoclay contents (<5 wt%) were found to exhibit much higher strength and modulus values than pure polyester fibers. In the cases of all polyester hybrid fibers, the values of the tensile mechanical properties were found to decrease linearly with increasing DR. However, the initial tensile modulus of the PTT hybrid fibers were found to be independent of DR.