First-principles calculations of the second-order optical response functions and the dielectric functions of urea [CO (NE:2)2] and some of its derivatives such as monomethylurea (H(2)NCONHCH(3), MMU), and N,N'-dimethylurea (H(3)CHNCO-NHCH(3), DMU) crystals are performed. On the basis of the density functional theory (DFT) in the local-density approximation (LDA), the highly accurate full-potential projected augmented wave (FP-PAW) method was used to obtain the electronic structure. Over a wide frequency range (0.0-10.0 eV), the dielectric constants and second-harmonic generation (SHG) susceptibilities of the urea crystal family have been obtained, and the results are in good agreement with the experimental values. The origin of the linear and nonlinear optical (NLO) properties of the urea crystal family has been analyzed by coupling the calculated electronic structure and optical spectrum. The prominent spectra of chi((2)) are successfully correlated with the dielectric function epsilon(omega) in terms of single-photon and double-photon resonances. The virtual electron (VE) and virtual hole (VH) processes have also been performed for the urea crystal family. From the research into the electron deformation density, crystal configuration, substitutional group, and so forth, it is found that the origin of the SHG of the urea crystal family is the charge transfer due to the strong "push-pull" effect along the hydrogen bond, which favors a head-to-tail arrangement of the molecules and enhances the SHG response. The electron-donating substitutional group supplies more electrons to the electron-accepting group, and helps to form large dipoles in molecules. The influence on the NLO properties of the local symmetry of the substitutional group is also discussed in detail.