Carbon Fiber Reinforced Polymer (CFRP) composites are broadly used in many engineering applications. Their inherent anisotropy due to different fiber orientations in the individual layers can be considered an advantage since the maximum strength of the composite component can be designated in preferential loading directions. However, this anisotropy leads to multiaxial stress conditions at the same time, complicating the damage sequence and the mechanical response of CFRPs. Identification of these multiaxial conditions at early loading stages is of paramount importance in order to predict the upcoming structural response of the material. Acoustic Emission (AE) is applied in this study to various CFRP composite laminates with different stacking sequences, in which different multiaxial conditions are generated. Laminates consisting of 30^o off-axis plies are characterized by dominant shear stresses, whereas in laminates with 60^o layers transverse normal stresses govern the stress state. Through quasi-static and incremental loading, it is shown through this research work that certain AE features can be used in order to identify the dominant stress component rather than just the occurring damage mode even at early loading stages, before severe fracture influences the mechanical capacity of the material. This is of great importance in cases that detrimental shear stresses are generated in the material, leading to important interlaminar delaminations and mechanical deterioration. AE can be used in this direction in order to predict the upcoming damage modes and to take the necessary measures to avoid final catastrophic failure.