Nonlinear feedback functional method is presented to realize synchronization of hyperchaos in higher dimensional systems. New nonlinear feedback functions and superpositions of linear and nonlinear feedback functions are also introduced to synchronize hyperchaos. The robustness of the method based on the flexibility of choices of feedback functions is discussed. By coupling well-known chaotic or chaotic-hyperchaotic systems in low-dimensional systems, such as Lorenz system, Van der Pol oscillator, Duffing oscillator and Rössler system, ten dimensional hyperchaotic systems are formed as the model systems. It can be found that there is not any noticeable difference in synchronization based on the numbers of positive Lyapunov exponents and of dimensions.