Diagnostic analyses of the enstrophy and the nonlinear cascade ofenstrophy are made in the wave-number domain, using data at the 500-hPa level for the summer of 1980. By comparing the results in our study with those shown by Steinberg, H. L. et al. for February-April, 1963,we find that the main characteristics of spectra distribution for summer and winter are much alike but the nonlinear exchanges of enstrophyamong waves for the two seasons are quite dissimilar. Steinberg emphasizes that enstrophy is transferred from the large to the smallerscale. Our study shows that, in summer, super-long waves (with num-ber of major waves equal to 3) supply enstrophy simultaneously to long(wave number=4-8) and short (wave number≥9) but meanwhile theshort waves transfer a great amount of enstrophy to the long waves,Ultimately, there is a net loss of enstrophy in the nonlinear exchangefor both the super-long and the short waves, with the former losingmore. And the long waves have a large net gain of enstrophy. Thus the sign of net gain or loss in enstrophy for long and short waves iscontrary to the winter case.