In this article, the notion of orthogonal nonseparable four-dimensional wavelet packets, which is the generalization of orthogonal univariate wavelet packets, is introduced. A new approach for constructing them is presented by iteration method. A novel approach for constructing two-directional biorthogonal wavelet packets is developed. The biorthogonality property of four-dimensional wavelet packets is discussed. Three biorthogonality formulas concerning these wavelet packets are estabished. A constructive method for affine frames of is proposed.