The transfer mechanism of applied stress in single-wall carbon nanotube (SWCNT)/poly(methyl methacrylate) (PMMA) nanocomposites was investigated using in situ Raman spectroscopy on composite fibers. These SWCNT/PMMA nanocomposite fibers have no specific SWCNT-polymer interactions and the high degree of nanotube alignment minimizes the contributions from nanotube-nanotube interactions. Although tensile testing found significantly improved overall mechanical properties of the fibers, effective stress transfer to SWCNTs is limited to a small strain regime (epsilon<0.2%). At higher strains, the stress on the SWCNTs decreases due to the slippage at the nanotube-polymer interface. Slippage was also evident in scanning electron micrographs of fracture surfaces produced by tensile testing of the composite fibers. Above epsilon = 0.2%, the strain-induced slippage was accompanied by irreversible responses in stress and Raman peak shifts. This paper shows that efficient stress transfer to nanotubes as monitored by Raman spectroscopy is crucial to improving the mechanical properties of polymer nanocomposites and to detecting internal damage in nanocomposites.