In this study, we present the convergence of time-varying networks. Then, we apply the convergence property to cooperative control of nonlinear multiagent systems (MASs) with unknown control directions (UCDs), and illustrate a new kind of Nussbaum-type function based control algorithms. It is proven that if the time-varying networks are cut-balance, the convergence of nonlinear MASs with nonidentical UCDs is achieved using the presented algorithms. A critical feature of this application is that the designed algorithms can deal with nonidentical UCDs by employing conventional Nussbaum-type functions. Finally, one simulation example is given to illustrate the effectiveness of the presented algorithms.