Thermoplastics are particularly well suited to the aerospace industry because of their superior mechanical properties and shelf-life when compared to thermosets. When manufacturing thermoplastic composite parts using automated fiber placement (AFP) technology, the high processing temperature and non-uniform cooling causes residual process stresses to arise. Constituent level or ply level stresses are residual stresses that come from interactions inherent to the composite system. They would be present in this carbon fiber reinforced polyether ether ketone (PEEK) material system regardless of the manufacturing method. Residual process stresses are laminate level stresses that arise from an external process, like AFP manufacturing. AFP manufactured parts can include flat panels with free edges and fully constrained geometries like rings and cylinders. They express their residual stresses somewhat differently: flat panels will warp visibly as they cool, while the stresses present in rings will only be visible once they have been slit along their length. They will visibly spring in or out. The goal of this thesis was to see if it was possible to use annealing to relieve the residual process stresses from thermoplastic composite structures manufactured using AFP without compromising laminate properties. These properties included crystallinity, void content, and fiber volume fraction. It would seem that the residual stresses in unidirectional panels with free edges can be mostly relieved with annealing. A 3-hour hold at 200˚C brought them to within 2mm of flat. However, the radii and spring-in or spring-out behavior of hoop-wound and asymmetric rings remained unaffected.