Nonlinear permutations of GF(2^n) with strong cryptographic properties have important applications in cryptology such as DES-like block ciphers, hush functions and stream ciphers. In paPer [1], we proved that the exponential function can provide a class of permutations satisfying the Strict Avalanche Criterion (SAC permutations) with algebraic nonlinear degree 2. In this paper, we further construct three classes of SAC permutations that are derived from the Dickson polynomials, GMW functions and the exponential functions with maximal algebraic nonlinear degree, respectively.