Fusion bonding is the principal phenomenon governing the fabrication of layered thermoplastic-matrix composites using techniques such as tow placement and tape laying. An important step in fusion bonding is the intimate contact process, which refers to the development of interfacial contact area between thermoplastic plies, caused by the spreading of the surface asperities. The contacted areas, in turn, form sites for molecular interdiffusion which leads to interfacial bonding. The geometric complexity of the surface asperity profiles presents a fundamental challenge to an effective description of the intimate contact process. Toward addressing the challenge, this paper presents a model for interfacial contact area development utilizing the fractal properties of thermoplastic ply surfaces. Using a Cantor set representation of the surfaces, and a squeeze flow model to describe their spreading during the processing, the interfacial contact area evolution is related to the process parameters and the geometric parameters in the fractal surface description. The model predictions are shown to compare well with experimental data for several thermoplastic materials.