Non-homologous end joining (NHEJ) is the dominant DNA double strand break (DSB) repair pathway and involves several repair proteins such as Ku, DNA-PKcs, and XRCC4. It has been experimentally shown that the choice of NHEJ proteins is determined by the complexity of DSB. In this paper, we built a mathematical model, based on published data, to study how NHEJ depends on the damage complexity. Under an appropriate set of parameters obtained by minimization technique, we can simulate the kinetics of foci track formation in fluorescently tagged mammalian cells, Ku80-EGFP and DNA-PKcs-YFP for simple and complex DSB repair, respectively, in good agreement with the published experimental data, supporting the notion that simple DSB undergo fast repair in a Ku-dependent, DNA-PKcs-independent manner, while complex DSB repair requires additional DNA-PKcs for end processing, resulting in its slow repair, additionally resulting in slower release rate of Ku and the joining rate of complex DNA ends. Based on the numerous experimental descriptions, we investigated several models to describe the kinetics for complex DSB repair. An important prediction of our model is that the rejoining of complex DSBs is through a process of synapsis formation, similar to a second order reaction between ends, rather than first order break filling/joining. The synapsis formation (SF) model allows for diffusion of ends before the synapsis formation, which is precluded in the first order model by the rapid coupling of ends. Therefore, the SF model also predicts the higher number of chromosomal aberrations observed with high linear energy transfer (LET) radiation due to the higher proportion of complex DSBs compared to low LET radiation, and an increased probability of misrejoin following diffusion before the synapsis is formed, while the first order model does not provide a mechanism for the increased effectiveness in chromosomal aberrations observed.