This paper presents the study of non-classical nonlinear response of fiber-reinforced composites. Nonlinear elastic wave methods such as nonlinearresonant ultrasound spectroscopy (NRUS) and nonlinear wave modulation spectroscopy have been used earlier to detect damages in several materials. It was observed that applying these techniques to composites materials becomes difficult due to the significant inherent baseline nonlinearity. Understanding the non-classical nonlinear nature of the composites plays a vital role in implementing nonlinear acoustic techniques for material characterization as well as qualitative nondestructive testing of composites. Since fiber reinforced composites are orthotropic in nature, the baseline response variation with fiber orientation is very important. This work explores the nature of the inherent nonlinearity by performing nonlinear resonant spectroscopy (NRS) in intact unidirectional carbon/epoxy samples with different fiber orientations with respect to major axis of the sample. Factors such as frequency shifts, modal damping ratio, and higher harmonics were analyzed to explore the non-classical nonlinear nature of these materials. Conclusions were drawn based on the experimental observations.