On the basis of INDO/SCI program, we have designed a program to calculate the nonlinear second - order polarizability B-ijk and B-mu according to the SOS expression. The electronic spectra and second order nonlinear optical properties of 1,2 - diamino - 4, 5 - dinitrobezene 1 and 1,3 - diamino - 4, 6 dinitrobezene 2 were studied. The calculated results indicate that molecule 1 possesses second - order nonlinear optical polarizability comparable to that of molecule 2. Because the dipole moment of 1 is much larger than that of 2, so the value of muB of 1 is much larger than that of 2. Based on the studied above, the electronic spectra and second - order nonlinear optical properties of 2,3 - bis - (beta - phenylethenyl) - 5,6 - dicyanopyrazine and 2,3 - bis - (beta - thienylethenyl) - 5,6 - dicyanopyrazine derivatives were studied as well. It is found that all these compounds possess two low - lying excited electronic states that are very close to each other in energies, both contributing to the second - order nonlinear optical polarizability in an additive fashion. These derivatives are good candidates as chromophores due to their absorption < 413 nm and large <mu>B values.