This study is concerned with structure-property relationships in different types of carbon nanotubes (CNTs), in particular investigating both interfacial and internal stress transfer for CNTs in nanocomposites. The shift of position and width of the G'-Raman band for single-walled CNTs (SWNTs) and multi-walled CNTs (MWNTs) in an epoxy matrix were used to monitor stress transfer between the nanotubes and an epoxy matrix in nanocomposites. It was found that the rate of band shift per unit strain was higher for the SWNTs than the MWNTs and that the G' band tended to undergo broadening with strain for the SWNTs and narrowing with strain for the MWNTs. A theory has been developed to simulate this behaviour in terms of stress transfer between the different layers within the MWNTs. It has also enabled the determination of the stress transfer efficiency parameter, (k (i)) for the MWNTs. It is demonstrated that MWNTs give inferior reinforcement to SWNTs as a result of slippage between the walls giving rise to poor internal stress transfer in the MWNTs. This phenomenon will lead to the MWNTs having a lower effective Young's modulus in nanocomposites than SWNTs.