The small-scale effect and the material nonlinearity significantly impact the mechanical properties of nanobeams. However, the combined effects of two factors have not attracted the attention of researchers. In the present paper, we proposed two new nonlocal theories to model mechanical properties of slender nanobeams for centroid locus stretching or inextensional effect respectively. Two new theories consider both the material nonlinearity and the small-scale effect induced by the nonlocal effect. The new models are used to analyze the static bending and the forced vibration for single-walled carbon nanotubes (SWCNTs). The results indicate that the stiffness softening effect induced by the material nonlinearity has more prominent impact than the nonlocal effect on SWCNT’s mechanical properties. Therefore, neglecting the material nonlinearity may cause qualitative mistakes.