In this article, we consider the distributed synchronization problem of dynamic networked systems with adaptive nonlinear couplings. Based on how the information is collected, the interactions between subsystems are characterized by nonlinear relative state couplings and nonlinear absolute state couplings. In both cases, we show that the considered nonlinear interactions can be used to simulate the couplings with disturbed relative or absolute states. In order to implement the nonlinear couplings in a fully distributed fashion, adaptive control laws are proposed for the adjustment of coupling strengths between connected subsystems. It is shown that the connected network topology is sufficient to ensure the synchronization of dynamic networked systems with the proposed adaptive nonlinear coupling methods. Different from many existing works, the σ-modification technique is used to suppress the increase of the coupling strengths with an additional benefit of preventing the coupling strengths from increasing. Simulation examples are given to assess the performance of the proposed adaptive nonlinear couplings.